text: (c) The first quartile. Standard deviation of Grouped Frequency Tables Recall that for grouped data we do not know individual data values, so we cannot describe the typical value of the data with precision. The general moments of $$R$$ can be expressed in terms of the gamma function $$\Gamma$$. Here is how to find the Interquartile Range from Normal Distribution when you are given the probability, the mean and standard deviation. The first quartile, or lower quartile, is the value that cuts off the first 25% of the data when it is sorted in ascending order. For pompano, the mean is 137 mm with a standard deviation of 27 mm 5 pts. Proof: expand and differentiate with respect to m. Understanding and Calculating the Standard Deviation Computers are used extensively for calculating the standard deviation and other statistics. Answer: The relationship between the mean, quartile and the standard deviation are as follows:. Standard deviation calculator For standard deviation calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). It will cut the list into four equal parts. First, second, and third quartiles refer to 25th, 50th and 75th percentile respectively. In the following R tutorial, I’ll show in three examples how to use the sd function in R. Djulbegovic, and I. Calculate the same measures for the Pittsburgh library. Interquartile Range Calculator Instructions. Where Q1: is the 1st quartile. Standard deviation measures the “dispersion of the data set” that is relative to its mean. 5 and the sample standard deviation is 2. The square root of Var(X) is called the standard deviation of X. find the mean of the squared deviations, 10/5 = 2, you have the variance, assuming that these five scores represent the entire population. Example 3: Use the formula to find the standard deviation of 5. Monthly aggregation. A quartile is an extended version of that and by dividing the data set in four parts, it deals with the spread of values above and below the mean. If the list of data a,b,c,d is in ascending or descending order, then the median is the average of b and c. 0000 75th Percentile: 5. Taking an average, we can calculate that the third quartile is 36. Select to return the 1st quartile (25th percentile) values for each key field combination. Calculate the mean of the sample. , discrete data and continuous data. 75 in Inv Norm (. Standard Deviation Versus Average Deviation. Square that deviation 5. Only use the mean and the standard deviation for reasonably symmetric distributions. The middle 50% of the exam scores are between what two values?. so lets calculate two standard deviations above the mean z=14. The normal calculator can be used to calculate areas under the normal distribution. 124 Standard Deviation 2011 8 February 16, 2011 Feb 168:52 AM The number of standard deviations a value is from the mean is called the ZScore. 5 (a constant used to discern outliers). The following calculator will find mean, mode, median, lower and upper quartile, interquartile range of the given data set. 8 of the Famous Shoeburger sandwiches for a given month. The standard deviation of the observations is given by: The standard deviation in our data is 8. average deviation = 0. We want to calculate the chance that her measurement will be over 140. Yes mean median, and the standard deviation could be determined with the help of Q1, Q2, and Q3 if the distribution does not diverge from the normal distribution. However, statisticians ran into. This quantity is called the variance and is equal to the square of the standard deviation. The mean is then found by taking this sum and dividing it by the number of scores. About Quartile Deviation Calculator. In descriptive statistics, the quartile deviation (QD) is half the difference between the third (upper) and first (lower) quartiles. It gives us an idea about the variability in a dataset. Step 3: Subtract Step 1 from Step 2. ; Q3 is 7 th term and product of 0. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. Text and Images from Slide. Enter the sample mean, the hypothesized mean,the sample size, and the sample standard deviation. The quartiles of a distribution are the three points that divide it into four equally numerous parts. 8 and (25-18)/6. 6 inches and a standard deviation of 2. Based on the quartile deviation, the Coefficient of Quartile Deviation can be defined, which makes it easy to compare the spread of two or more different distributions. Originally, SAT tests had a mean score of 500 with a standard deviation of 100, while ACT tests had a mean score of 18 with a standard deviation of 6 (these are no longer the means and standard deviations for thosae tests). Determine the first quartile and the third quartile. Yes mean median, and the standard deviation could be determined with the help of Q1, Q2, and Q3 if the distribution does not diverge from the normal distribution. Find the first and third quartiles and the five number summary. The graph depicts the standard normal distribution with mean O and standard deviation 1, -3. 7% within 3 standard deviations of the mean. 6) ( ) 21 29 × + × + = 1192. The ﬂve number summary is usually better than the mean and the standard deviation for describing skewed distributions. Return the harmonic mean of data, a sequence or iterable of real-valued numbers. You can display some of these statistics individually, such as the mean and median. Hello friends! Today we shall share with you how you can calculate the standard deviation for ungrouped data. What is the inter-quartile range? 1072 346. Consider the following numeric vector in R:. 19 28) Calculate the range of the following data set: 7, 8, 4, 1, 4, 15, 5, 8, 5. What additional information is needed to construct a box plot for the FTES for 2005-2006 through 2010-2011 and box plot for the FTES for 1976-1977 through 2004-2005? 102. The probability of a random variable falling within any given range of values is equal to the proportion of the area enclosed under the function’s graph between the given values and above the x -axis. Quick Calculator Search. s = sample standard deviation; σ = population standard deviation; f = frequency; Σ = sigma (means summation) CV = coefficient of variation; MAD = mean absolute deviation or mean deviation; z = z score (standard score or standardized score) Q 1 = lower quartile or 1st quartile; Q 2 = middle quartile or 2nd quartile or median; P 50 = 50th. (c) The first quartile. select_kth(ARRAYREF, K). By using this website, you agree to our Cookie Policy. The square root of Var(X) is called the standard deviation of X. While there are several different types of mean, we will focus on the arithmetic average. 67, and the standard score of the third quartile, z 3 , is +0. {: Returns the Mean and Variance of the Values, assuming a Population. (d) The second (median) quartile. lumenlearning. Quartile deviation is the difference between “first and third quartiles” in any distribution. Calculate variation from the mean. The interquartile range of an observation variable is the difference of its upper and lower quartiles. Box-and-Whisker Plot. This online calculator calculates mean, variance and standard deviation of random variable entered in the form of value-probability table person_outline Timur schedule 2018-01-22 03:29:41 This calculator can help you to calculate basic discrete random variable metrics: mean or expected value , variance , and standard deviation. A quick and easy how-to guide for finding measures of central tendency relating to statistics such as the mean, median, mode, range, standard deviation, first quartile, third quartile, sum, max, and min in Microsoft Office Excel 2010. Basic Stats on Data from Calculator. Calculates the median absolute deviation (MAD) in what I believe is O(n). The calculation of standard deviation will be based on the sample standard deviation formula ( )2 1 xx s n − = −. For example: 601. Exercise 2Find the standard deviation for. Subtract the mean from your score. Calculate the sample mean and the sample standard deviation to one decimal place using a TI-83+ or TI-84 calculator. Where − ${k = \frac{the\ within\ number}{the\ standard\ deviation}}$ and ${k}$ must be greater than 1. Standard deviation measures the “dispersion of the data set” that is relative to its mean. Variance is equal to the standard deviation squared. Standard deviation of Grouped Frequency Tables Recall that for grouped data we do not know individual data values, so we cannot describe the typical value of the data with precision. Generally speaking in a data set with a normal distribution (i. A quartile is an extended version of that and by dividing the data set in four parts, it deals with the spread of values above and below the mean. The Mu and Sigma above is population mean and Standard deviation and not of sample. The interquartile range is the distance between the third and the first quartile, or in other words IQR = Q3- Q1. For example, the mean of the numbers 4, 5, 5, 6 and 40 is the sum of the numbers, 60, divided by 5. Mohawk Valley Community College Learning Commons IT129. Interquartile Range Calculator Instructions. If P is normally distributed, then the standard score of the first quartile, z 1 , is −0. Note: Values in the given data sets will represent samples of larger populations. 25) gives the exact same result. So this is gonna give us our inter quartile range. The formulas used to calculate the mean for grouped data are as follows. Find the quartiles of the eruption durations in. sqrt() to calculate the power and square root respectively. Square root – now the value is in the units we started with!!!. Decision making The data set having higher value of quartile deviation has higher variability. Here's something from the link below. normal distribution with mean μ and standard deviation σ. What is the range? 11. Basic Stats on Data from Calculator. For example, if you scored 33 and the mean is 24, you would get a difference of 9. For pompano, the mean is 137 mm with a standard deviation of 27 mm 5 pts. Introduction: The boxplot or a box-and-whisker plot is a graphical representation of a data set. Decision making The data set having higher value of quartile deviation has higher variability. (2) (Total 6 marks) 8. A low standard deviation for a variable indicates that the data points tend to be close to its mean, and vice versa. How many have ages between 24 and 32 years? Find the age such that 75% is below it. Find the probability that a sexual assault occurs on the average between 1. Press SHIFT MODE , then arrow down to the next list of options. Step 2: Find the third quartile, Q 3. Equivalently, X=eY where Y is normally distributed with mean μ and standard deviation σ. The same method is also used by the TI-83 to calculate quartile values. Standard deviation can never be negative as it is a measure of distance (and distances can never be negative numbers). third quartile = 1158, fourth quartile = 1499. See also Standard Deviation Explained for. The sum of all of the displayed array's values. They do not have to be integers. First the median and quartile values are calculated. Taking an average, we can calculate that the third quartile is 36. Values must be numeric and may be separated by commas, spaces or new-line. Standard deviation can never be negative as it is a measure of distance (and distances can never be negative numbers). Based on the quartile deviation, the Coefficient of Quartile Deviation can be defined, which makes it easy to compare the spread of two or more different distributions. Calculates the median absolute deviation (MAD) in what I believe is O(n). 0 inches and standard deviation of 3. Identify the mean, median and standard deviation in skewed or normal histograms. 75 in Inv Norm (. Mean Deviation = 4/5 × Quartile deviation Standard Deviation = 3/2. Using sample data, students will make informal references about population means and standard deviations. STD_QRANGE. If Q 1 is the first quartile and Q 3 is the third quartile, then the formula for deviation is given by;. Typically, the quartiles are indicated by uppercase Q s, with the subscript indicating which quartile we are talking about ( Q 1 is the first quartile and Q 3 is the third quartile). 5 + 8 + 2 + 1 = 16. Again, the difference of the variance between the 3 rd and 1 st quartiles is termed as the. This quartiles calculator also finds out median, greater value, lowest value as well as the total sum for the given set of data. Calculate the same measures for the Pittsburgh library. The mean and standard deviation are used to summarize data with a Gaussian distribution, but may not be meaningful, or could even be misleading, if your data sample has a non-Gaussian distribution. Five number summary is a descriptive statistics. The relationship between the two is depicted below:. Once we've calculated the first and third quartiles, we'll often want to calculate the interquartile range. For the variance and standard deviation statistics, it is important to know if you are looking at a sample or the entire population of possible items. Again, the difference of the variance between the 3 rd and 1 st quartiles is termed as the. Before I show you how to get the line of best fit, let’s get some simple data on the two sets of data – like the mean, median, quartiles, and max (that we got by hand for our Box and Whisker Plot earlier in the Introduction to Statistics and Probability section). Difference between upper (third) and lower (first) quartiles; Quartiles divide data into 4 equal groups. By using this calculator, user can get complete step by step calculation for the data. The Quartile Deviation is a simple way to estimate the spread of a distribution about a measure of its central tendency (usually the mean). Step 2: Find the third quartile, Q 3. 6687 Moreover, quartile deviation is not affected by the extreme values where it contains extreme values. The calculation of variance is basically the same as it was for standard deviation — only without STEP #6, taking the square root. Find the value that is two standard deviations below the mean. select_kth(ARRAYREF, K). The interquartile range is the distance between the third and the first quartile, or in other words IQR = Q3- Q1. The mean can be found by dividing the sum of the scores by the number of scores. How does the shape of the distribution affect the mean and median? 10. mean of the squared deviations from the mean, or the square of the standard deviation; for a set of data, a deviation can be represented as $$x$$ – $$\bar{x}$$ where $$x$$ is a value of the data and $$\bar{x}$$ is the sample mean. We want to calculate the area to the right. The range e. 0 and the unbiased standard deviation was 3. Hence one could compare 680 on the SAT with 25 on the ACT. When reporting the results of clinical studies, some researchers may choose the five‐number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation (SD), particularly for skewed data. Find the value that is one standard deviation above the mean. How do you find the outlier with mean and standard deviation? Variance, Standard Deviation, and Outliers - What is the 1. we find the mean and standard deviation of the all the data points An outlier is a point which falls more than 1. Each score’s deviation from the mean 4. Originally, SAT tests had a mean score of 500 with a standard deviation of 100, while ACT tests had a mean score of 18 with a standard deviation of 6 (these are no longer the means and standard deviations for thosae tests). It can never be negative. Definition: The variance of a set of data is the average of the square distances that each data point lie from the mean. Use the calculator to find the proportions. There are three quartiles: the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3). The z-score is the number of standard deviations from the mean. And we get 2. Mohawk Valley Community College Learning Commons IT129. For q3, since 75% of the scores are below this value and since the area under the curve is 1, the area below the score representing the 75th percentile is 0. In other words the standard deviation is the square root of the variance of all individual values from the mean. When reporting the results of clinical studies, some researchers may choose the five‐number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation (SD), particularly for skewed data. The other name for quartile is basically cuts. Approximately 68% lies within 1 standard deviation of the mean; 95% within 2 standard deviations; and 99. The calculator will generate a step by step explanation on how to find these values. will be – QD = 15. We cannot determine if any of the third quartiles for the three graphs is different. Notice the difference between the codes of quartiles and deciles computations. Challenge: Analyze Temperature Statistics 1. How to (Really) Calculate Standard Deviation Video of How to (Really) Calculate Standard Deviation We’ve now talked about three methods for calculating average values: the mean , median , and mode (affectionately known as the three Ms). In addition to showing median, first and third quartile and maximum and minimum values, the Box and Whisker chart is also used to depict Mean, Standard Deviation, Mean Deviation and Quartile. Find quartile 3 which is the IQ score seperating the top 25% from the others---Find the z-value that has a left-tail of 0. That will tell us the "center" of the distribution of values and the "spread" around that center. There are three quartiles: the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3). The Quartile Deviation Calculator is used to calculate the quartile deviation of a set of numbers. The standard deviation and its close relative, the variance, measure spread by looking. Data values other than the mean will be less probable. The following calculator will find mean, mode, median, lower and upper quartile, interquartile range of the given data set. This measure is widely used for studying dispersion. The sum of the scores is divided by the number of values (N=100 for this example) to estimate the mean, i. QD = [Q3 - Q1]/2 Box Plots: A graphical display based on quartiles that helps to picture a set of data. To calculate the quartiles and IQR * Quartile 1 (Q1) = 25% = While non-robust statistics like mean and standard deviation are useful for describing symmetric distributions. half of the interquartile range (IQR). Given the following contingency table: BST. Step 1: Order from low to high. Quartile deviation using numpy. The third quartile should be greater than 15 observations and less than five. Hence outliers will effect standard deviation. Press SHIFT MODE , then arrow down to the next list of options. Generally speaking in a data set with a normal distribution (i. 5 (a constant used to discern outliers). The standard deviation for (b) is larger than the standard deviation for (a). However, the standard deviation can be more easily interpreted because the unit for the standard deviation is the same than the unit of measurement of the data (while it is the. · Create a box-plot for the “Annual Sales” variable. The property of the standard deviation is such that when the underlying data is normally distributed, approximately 68% of all values will lie within one standard deviation on either side of the mean, and approximately 95% of all values will lie within two standard deviations on either side of the mean. Use this online interquartile range calculator to find the values of first quartile, third quartile, median and inter quartile range. The mean and the median are essentially equal. VARIANCE AND STANDARD. Definition: The variance of a set of data is the average of the square distances that each data point lie from the mean. 05 to reject the null hypothesis that there is no difference in the mean for the data and the stated value. Use the function boxplot() to plot the boxplot of GC content for all genes. (+/-) One standard deviation away from the mean accounts for somewhere around 68 percent of the people in this group. For example, you can use it to find the proportion of a normal distribution with a mean of 90 and a standard deviation of 12 that is above 110. Quartile Deviation = (Third Quartile – First Quartile) / 2 Quartile Deviation =(Q 3 – Q 1 ) / 2 While the coefficient of quartile deviation is used to compare the variation between two data sets. Djulbegovic, and I. You have collected data from a number of charities. Once we've calculated the first and third quartiles, we'll often want to calculate the interquartile range. Typically, the quartiles are indicated by uppercase Q s, with the subscript indicating which quartile we are talking about ( Q 1 is the first quartile and Q 3 is the third quartile). The Mu and Sigma above is population mean and Standard deviation and not of sample. The scores on the exam have an approximate normal distribution with a mean μ = 81 points and standard deviation σ = 15 points. College professors can have between 0 and 40 (or possibly 50) years of experience. (Assume the data set has a bell-shaped distribution. Square root the Variance to get Standard Deviation } procedure PopulationVarianceAndMean (const X: array of Extended; var Variance, Mean: Extended); {: Returns the Median (2nd Quartiles) of the Values. The IQR (interquartile range) is then calculated as the difference between the first and third quartile values. If the standard deviation were. 05 to reject the null hypothesis that there is no difference in the mean for the data and the stated value. If P is normally distributed, then the standard score of the first quartile, z 1, is −0. - Use these values to calculate the z-values for all data point. The interquartile range of an observation variable is the difference of its upper and lower quartiles. A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 126 with standard deviation of 18, and the mean length of two-year-old spotted flounder is 162 with a standard deviation of 28. a) Calculate the mean, median, mode, first quartile and third quartile. This page estimates the mean, variance, and standard deviation of a sample on the basis of the sample’s reported median and range according to the method devised by S. For the dataset, (290) 10 1. This quartile calculator and interquartile range calculator finds first quartile Q 1, second quartile Q 2 and third quartile Q 3 of a data set. Quartiles and the Interquartile Range Quartiles. , the difference between Q 3 and Q 1 in a five-number summary) • 5-number summary – a summary that provides information about a data set and contains five values: the minimum (smallest value), first quartile, median (middle value), third quartile. The arithmetic mean d. Quartile deviation using numpy. Press calculate and the sample standard deviation for the list will be calculated. This rule should be applied only when the data are approximately normal. A quartile is an extended version of that and by dividing the data set in four parts, it deals with the spread of values above and below the mean. Solution: (B) If you look at the formula for standard deviation above, a very high or a very low value would increase standard deviation as it would be very different from the mean. Introduction: The boxplot or a box-and-whisker plot is a graphical representation of a data set. In the above program, we've used the help of Java Math. To calculate the percentile, you will need to know your score, the mean and the standard deviation. In a boxplot, the 'box' is bounded by the first quartile at the bottom or left, and the third quartile at the top or right, with a line representing the median being represented within the box. Solution to Example 1 We first order the data set in ascending order. standard deviation for Gini’s mean difference. For these studies, when included in a meta-analysis, it is often desired to convert the five-number summary back to. a distribution into a traditional bell curve), some 68% of the data should fall within one standard deviation of the mean and a. Variance and Standard Deviation: Variance and Standard Deviations are closely related. The last column in the table above shows the absolute deviations. For more on standard deviation, see the wikiHow article How to Calculate Standard Deviation. If P is normally distributed, then the standard score of the first quartile, z 1 , is −0. Deviation •Coefficient of variation The coefficient of variation indicates how large the standard deviation is in relation to the mean. Quartile deviation which is also renowned as a semi interquartile range. Med the median. The result will be presented as a real or a timespan, depending on the data type of the argument. The Whiskers connect the minimum and the maximum values to the Box. (d) The second (median) quartile. Calculate a percentile from a quantitative data set. The average squared deviation from the mean is also known as the variance. Use of the Frequency Table When a frequency table is given, we can use new formulas to compute the mean and variance of the data. Histogram generation according to input data. 2 Find the mean and the standard deviation of the set of numbers 5, 8,8,9,14,18,100. This quartile calculator and interquartile range calculator finds first quartile Q 1, second quartile Q 2 and third quartile Q 3 of a data set. Relevant Equations: Let x = data value, n = sample size. The 50 th percentile is the median. Xiang Wan, Wenqian Wang, Jiming Liu and Tiejun Tong (2014), "Estimating the sample mean and standard deviation from the sample size, median, range and/or interquartile range", BMC Medical Research. Generally speaking in a data set with a normal distribution (i. When you using the normal distribution, and you got a mean of 0 and standard deviation of 1 you have what is known as the Standard Normal Distribution. · Create a box-plot for the “Annual Sales” variable. Although the mean and standard deviation are often used to summarize a set of data, much information is lost in this approach, particularly related to the shape of the graph. We want to calculate the chance that her measurement will be over 140. The standard deviation is interpreted with respect to the mean. Data 1 has more data values above 2 than Data 2 has above 2. 07, and the sample MDs varied from 2. Standard deviation is significantly affected by outliers. 0530 D) 143. If the most extreme data has 1. You have collected data from a number of charities. Here is how to find the Interquartile Range from Normal Distribution when you are given the probability, the mean and standard deviation. Calculate the first- and third-quartile scores for this exam. will be – QD = 15. Similarly, first, second, third, and fourth quintiles refer to 20th, 40th, 60th, and 80th percentile respectively. When reporting the results of clinical studies, some researchers may choose the five‐number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation (SD), particularly for skewed data. The third quartile, or the upper quartile, is the value. For a particular sample of 68 scores on a psychology exam, the following results were obtained. A fish story: The mean length of one-year-old spotted flounder, in millimeters, is 126 with standard deviation of 18, and the mean length of two-year-old spotted flounder is 162 with a standard deviation of 28. It will put the complete list of numbers in an order. Calculate the sample variance of these ages. Variance describes, mathematically, how close the observations in a data set (data points) are to the middle of the distribution. 6 inches) from the mean (54 inches). Quartile deviation using numpy. the third quartile, Q 3. Enter data separated by commas or spaces. This measure is used to analyze the difference of spread in the data relative to the mean or average value. Norm(Area to the left, mean, standard deviation) ENTER 9) Women's and Men's heights again - Women's heights are normally distributed with a mean of 65. 7% within 3 standard deviations of the mean. 5 and the sample standard deviation is 2. 95% of the observations fall within two standard deviations of the mean. Let z=μ +- nσ where μ is the mean and σ is the standard deviation and n is the multiple above or below. Minus quartile, same data set. Standard deviation measures the “dispersion of the data set” that is relative to its mean. Step 3: Subtract Step 1 from Step 2. P is the probability that the mean for the data equals the value you were comparing it to. A quick and easy how-to guide for finding measures of central tendency relating to statistics such as the mean, median, mode, range, standard deviation, first quartile, third quartile, sum, max. Mohawk Valley Community College Learning Commons IT129. Gauss g-test. True or False: In a boxplot, the box portion represents the data between the first and third quartile values. In case population mean and standrad deviation is not known then sample mean and standard deviation can be used. Find the quartiles of the eruption durations in. The standard deviation of the mean (SD) is the most commonly used measure of the spread of values in a distribution. 8907 3108 oo C) 0. The calculation of variance is basically the same as it was for standard deviation — only without STEP #6, taking the square root. The standard deviation is defined as the positive. 9 and population standard deviation of 0. to calculate the numerical variability of the population from the central tendencies like mean of the data. Square that deviation 5. Does it look symmetric? Would you prefer the IQR instead of the standard deviation to describe this variable’s dispersion? Why?. Calculate the 1st, 2nd, and 3rd quartiles of the box weight. The variance is a measure of dispersion around the mean, equal to the sum of squared deviations from the mean divided by one less than the number of cases. In other words the standard deviation is the square root of the variance of all individual values from the mean. Use the Empirical Rule to find the percentage of adults with scores between 70 and 130. The grouped data can be divided into two, i. Here is how to find the Interquartile Range from Normal Distribution when you are given the probability, the mean and standard deviation. Note the size and location of the mean$$\pm$$standard deviation bar. A simple, easy to use statistics calculator for android. This quartile calculator and interquartile range calculator finds first quartile Q 1, second quartile Q 2 and third quartile Q 3 of a data set. If you choose to use the calculator, Q 3 is equal to the 75th percentile. Square root – now the value is in the units we started with!!!. This is the nice feature of the standard score -- no matter what the original scale was, when the data is converted to its standard score, the mean is zero and the standard deviation is 1. Scatterplot with Line of Best Fit. Introduction: The boxplot or a box-and-whisker plot is a graphical representation of a data set. This distribution is very common in real world processes all around us. 0000 75th Percentile: 5. 0 inches and standard deviation of 3. As a result, the numbers have a standard deviation of zero. Exercise 16. The standard deviation is defined as the positive. 85 kg from Problem 1 of Exercise 327 Standard deviation, σ = {fx x( )} f − ∑ ∑. SD and Var for a Population. 50), enter 0 then COMMA then 1. In practice, we rarely know the population standard deviation. To calculate the percentile, you will need to know your score, the mean and the standard deviation. Problem Statement: Use Chebyshev's theorem to find what percent of the values will fall between 123 and 179 for a data set with mean of 151 and standard deviation of 14. The further the other values are from the mean the less probable they are. This quantity is called the variance and is equal to the square of the standard deviation. For example, you can use it to find the proportion of a normal distribution with a mean of 90 and a standard deviation of 12 that is above 110. 50% of the population data lies here. High School Stats Chapter 2 Chapter Review. Only use the mean and the standard deviation for reasonably symmetric distributions. Standard Deviation. If x is a matrix, calculate statistics over the first non-singleton dimension. , the number m that minimizes E[(X-m)^2] is m=E(X). Note 2B † Box Plots The calculator can display up. 5 and the difference between 8 th and 7 th term which is (18-16)*0. Mean, Median & Mode. Let's look at the following 10. The mean of the standard scores is zero and the standard deviation is 1. The standard deviation of the mean (SD) is the most commonly used measure of the spread of values in a distribution. If there is no variation at all, the standard deviation will be zero. 67, and the standard score of the third quartile, z 3, is +0. (a) What is the first quartile score for this exam? Answer: (b) What is the third quartile score for this exam? Answer:. the product of two variables, each with values of 1, 2, 3, or 4, corresponding to increasing quartiles of pesticide use and neighborhood poverty), while controlling for household poverty and other. The mean is then found by taking this sum and dividing it by the number of scores. The more variation in the data, the higher the standard deviation will be. Interquartile Range Calculator Instructions. 78 years old. Range and Quartile Deviation measure the dispersion by calculating the spread within which the values lie. Once we've calculated the first and third quartiles, we'll often want to calculate the interquartile range. Maximum volume of the sample allowed is 100 000 values. What is the range? 11. For example, if A is a matrix, then std(A,0,[1 2]) computes the standard deviation over all elements in A , since every element of a matrix is contained in the array slice defined by dimensions 1 and 2. Standard Deviation & Mean. The short cut is just read the first quartile (Q1) value and the third quartile (Q3) value from the box and whisker plot. 9 and the sample standard deviation = 4. 2) Find the values of the 3rd quartile (Q3) and the 1st quartile (Q1) values by using the locator's formula: c = k(n)/4. Further, they could be given as the upper quartile or the lower quartile. 5 standard deviations from (below and above) the mean. When reporting the results of clinical studies, some researchers may choose the five‐number summary (including the sample median, the first and third quartiles, and the minimum and maximum values) rather than the sample mean and standard deviation (SD), particularly for skewed data. Write the distribution in proper notation, and calculate the theoretical mean and standard deviation. 9 and population standard deviation of 0. 4*10*16) = 0. Norm(Area to the left, mean, standard deviation) ENTER 9) Women's and Men's heights again - Women's heights are normally distributed with a mean of 65. There are three quartiles: the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3). The z-score is the number of standard deviations from the mean. To find the value of mean, divide this sum by the total number of observations in the data. Which measure of central tendency is calculated by summing the values and dividing by the number of values? a. Explanation: the numbers are all the same which means there's no variation. Mean deviation from median is always less. This calculates the third quartile in that dataset and this calculates the first quartile in that dataset. The standard deviation can be negative. Mean and standard deviation. So if your data set is in L1, enter L1 (2 nd key 1). estimate of the standard deviation, based on interquartile range. Sample some of these worksheets for free!. The standard deviation helps in detecting outliers, or elements of the data set that stray too far from the mean. Example of two calculations. Here is how to find the Interquartile Range from Normal Distribution when you are given the probability, the mean and standard deviation. Calculates the third quartile. lumenlearning. Problem Statement: Use Chebyshev's theorem to find what percent of the values will fall between 123 and 179 for a data set with mean of 151 and standard deviation of 14. 5 x (IQR) to the third quartile. In my classes students tend to mix up the information presented in: A boxplot (Quartiles) Errorbar (Mean+/-2 Standard Deviation, about 95%) The main reason is that in both cases percentages play an important role. IQR = Q3- Q1. From the sample we calculate the statistics. In the above program, we've used the help of Java Math. Descriptive Statistics Sample has 28 observations. For q3, since 75% of the scores are below this value and since the area under the curve is 1, the area below the score representing the 75th percentile is 0. 5 Quartiles and Percentiles. The formulas used to calculate the mean for grouped data are as follows. The mean is: The median is: The sample standard deviation is: The first quartile is: The third quartile is: What percent of the respondents have at least 5 pairs of Shoes? % 49% of all respondents have fewer than how many pairs of Shoes?. The standard deviation is a measure of the spread of the data. If you like to receive aggregated. The interquartile range is the distance between the third and the first quartile, or, in other words, IQR equals Q3 minus Q1. Note 2B † Box Plots The calculator can display up. College professors can have between 0 and 40 (or possibly 50) years of experience. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. Med the median. There are three quartiles: the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3). Find the median, the first quartile, and the third quartile for the sample mean time of sexual assaults in the United States. The larger the standard deviation, the the individual value are fro. 8 and (25-18)/6. With this method, the first quartile is the median of the numbers below the median, and the third quartile is the median of the numbers above the median. PERCENTILE(A1:A20,0. However, statisticians ran into. So now we wanna select it again. 80 × standard deviation; where 0. How many have ages between 24 and 32 years? Find the age such that 75% is below it. Mean absolute deviation: Before we all delve into this, it worth noting to really understand what ‘deviation’ really mean. The standard deviation of the mean (SD) is the most commonly used measure of the spread of values in a distribution. Inter-quartile ratio. Exercise 16. Calculate the first- and third-quartile scores for this exam. – This is the standard deviation of the variable. The Quartile Deviation Calculator is used to calculate the quartile deviation of a set of numbers. Find the zscore of the value 76. Statistics - Quartile Deviation - It depends on the lower quartile ${Q_1}$ and the upper quartile ${Q_3}$. Note: The second argument of the QUARTILE function must be a number between 0 and 4. IQR is the difference between the value of the 75 th and the 25 th percentile (or the first and the third quartile, hence the name). Find the median, the first quartile, and the third quartile for the sum of sample times of sexual assaults in the United States. There are three quartiles: the first quartile (Q1), the second quartile (Q2), and the third quartile (Q3). 5 times the difference between. Calculate the sample variance of these ages. Very important to remember: Always arrange from lowest to highest all the given data points if you are using manual method. Refer to the following box plots. Since it. pow() and Java Math. A’ 25 35 10. Thus if µ x = µ y the combined population variance would be. First the median and quartile values are calculated. Since height measurements are described by a normal curve, the doctor can know that 68% of all 10-year old boys are within one standard deviation (2. Variance tells us that how far away are the values from the mean. The following calculator will find mean, mode, median, lower and upper quartile, interquartile range of the given data set. As you know, a standard deviation is an important concept used by statisticians, financial advisors, mathematicians, etc. 3rd Quartile. To move from discrete to continuous, we will simply replace the sums in the formulas by integrals. Using the formula given above, the trimean is computed as (161 + 2(166) + 171)/4 = 166. This quartile calculator uses McCabe's formula that does not take account of the median of the data set when computing the 1 st and the 3 rd quartiles. Each score’s deviation from the mean 4. The sum of the scores is divided by the number of values (N=100 for this example) to estimate the mean, i. A single extreme observation can radically change the mean, standard deviation, and skewness of data. 7% of the. The interpretation of percentages. The mean length of a bluefish is 264 millimeters with a standard deviation of 60 mm. Square root the Variance to get Standard Deviation } procedure PopulationVarianceAndMean (const X: array of Extended; var Variance, Mean: Extended); {: Returns the Median (2nd Quartiles) of the Values. The mean IQ score of adults is 100, with a standard deviation of 15. If P is normally distributed, then the standard score of the first quartile, z 1, is −0. Draw a normal distribution centered about 125 with standard deviation 10. BMI Calculator » Triangle Calculators » Length and Distance Conversions » SD SE Mean Median Variance » Blood Type Child Parental Calculator » Unicode, UTF8, Hexidecimal » RGB, Hex, HTML Color Conversion » G-Force RPM Calculator » Chemical Molecular Weight Calculator » Mole, Moles to Grams Calculator » R Plot PCH Symbols » Dilution. For example: 601. A quick and easy how-to guide for finding measures of central tendency relating to statistics such as the mean, median, mode, range, standard deviation, first quartile, third quartile, sum, max. So a Normal distribution with the same mean and standard deviation would have a third quartile larger than the actual Q3. In the example above, 1 standard deviation is 21 + 8. 105, 145, 190, 140, 175 A) 171. 6^2*10^2 + 0. Five pieces of data are needed to construct a box plot: The minimum Value; The first quartile; The median; The third quartile; The maximum value. Example: Find the z-score or z value of a normal variable whose value is 45 if its mean is 50 and standard deviation is 5. 7 Measuring Spread: The Standard Deviation The five-number summary is not the most common numerical description of a distribution. • Here’s how to calculate the mean absolute deviation. Seperate the list with spaces, ex: 1. For each data value, absolute deviation is just the absolute value of the actual deviation from the mean of the distribution. Quartile deviation calculator For quartile deviation calculation, please enter numerical data separated with comma (or space, tab, semicolon, or newline). The third quartile, or upper quartile, is the value that cuts off the first 75%. The standard deviation of wages in dollars cannot be compared with the standard deviation of amount of meat in kilograms. Summary statistics find mean and standard deviation. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. It measures dispersion around the average. The median c. Online calculator. The average squared deviation from the mean is also known as the variance. Since height measurements are described by a normal curve, the doctor can know that 68% of all 10-year old boys are within one standard deviation (2. 2nd Vars (Distr)>"InvNorm" next you subtract 1-% and enter this into your Inverse Norm along with your Mean and standard deviation. 2500 Interquartile Range: 2. An online quartile calculator that helps to calculate the first quartile (q1), second quartile (q2), third quartile (q3), & interquartile range from the data set. , the number m that minimizes E[(X-m)^2] is m=E(X). Calculate the sample mean and the sample standard deviation to one decimal place using a TI-83+ or TI-84 calculator. According to Google. The first quartile Q 1 is the median of the observations located to the left of the median in the ordered list. To move from discrete to continuous, we will simply replace the sums in the formulas by integrals. In the first data series, the CV is nearly 50%. quartile, the median, the third quartile, and the largest observation. The mean deviation is defined as a statistical measure which is used to calculate the average deviation from the mean value of the given data set. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. For example, to calculate P(0<=Z<=1. Mohawk Valley Community College Learning Commons IT129. Again, the difference of the variance between the 3 rd and 1 st quartiles is termed as the. In the past, when the sample size was large, this did not present a problem to statisticians. Calculate the Percentile from Mean and Standard Deviation. Gina and Stewart are surf-fishing on the Atlantic coast, where both bluefish and pompano are common catches. the mean of 100 + or – 16), while just over 95% of the population would have IQ test scores between 68 and 132 (i. Each part has approximately the same number of items. The mean is: The median is: The sample standard deviation is: The first quartile is: The third quartile is: What percent of the respondents have at least 5 pairs of Shoes? % 49% of all respondents have fewer than how many pairs of Shoes?. Quartile Formula Quartiles are given as values dividing the complete list into quarters. The following calculator will find mean, mode, median, lower and upper quartile, interquartile range of the given data set. On the TI-83/84 Calculator we can use the 1-Var Stats to find the standard deviation on the list of statistics as Sx=11. What is data variance and standard deviation? Different values in the data set can be spread here and there from the mean. Is the range a resistant measure of spread? Explain. 1st Quartile. The quartiles of any distribution are1lie values with cumulative proportions 0. For example, to calculate P(0<=Z<=1. In other words, Variance is the average of all squared deviations. Standard deviation could be equal to one and be considered large or it could be in the millions and still be. In this example, 34. Standard deviation and variance are often used interchangeably and both quantify the spread of a given dataset by measuring how far the observations are from their mean. 27) The top speeds for a sample of five new automobiles are listed below. This gives information regarding the spread of the distribution of the variable. All the summation part of the equation means is that we subtract our mean from each number in the set, square that value, and then add all of those values for each number together. Variance tells us that how far away are the values from the mean. Scatterplot with Line of Best Fit. Variance: Calculated by taking the deviation of each value in the dataset from the mean and then squaring it. To calculate the percentile, you will need to know your score, the mean and the standard deviation. The third quartile or 75th percentile, x H (Q 3) is the value such that 75% of the observations are less than x H. Even discounting the outliers, the range of values in the 4th quartile is larger than that of the other quartiles. 5 and the sample standard deviation is 2. 8; so there is a 68% probability that a location will sell between 12. It divides roughly 25% of the largest items from the rest of the dataset. First the median and quartile values are calculated. Two of the most popular ways to measure variability or volatility in a set of data are standard deviation and average deviation, also known as mean. cal research, instead of reporting the sample mean and standard deviation of the trials, some trial studies only report the median, the minimum and maximum val-ues, and/or the first and third quartiles. The properties of quartiles are noted below. Calculates the median absolute deviation (MAD) in what I believe is O(n). How do I calculate the mean and standard deviation and use these measures to compare data sets? Standard – MM2D1. Now, calculate other popular statistical variability metrics and compare them to the standard deviation! For instance, the variance of this dataset is 1256. Originally, SAT tests had a mean score of 500 with a standard deviation of 100, while ACT tests had a mean score of 18 with a standard deviation of 6 (these are no longer the means and standard deviations for thosae tests). For any data set, if we add a score equal to the mean, the value of the mean will not change, but the standard deviation will become smaller • If the value added is equal to the mean, it has no distance from the mean and therefore adds nothing to the sum of the differences from the mean • However, by adding a score equal to the mean, we are. Both formula are accepted ways to calculate quartiles, although the former is becoming standardized in statistical software. To calculate the percentile, you will need to know your score, the mean and the standard deviation. 5 and the result is 16 + 1 = 17. This time the function quantile has an argument type which is set to 5. Please input numbers in the required fields and click CALCULATE. In simple words: SQRT(variance) = Standard Deviation. The interquartile range is the difference between the third quartile (Q3) and the first quartile (Q1). Introduction: The boxplot or a box-and-whisker plot is a graphical representation of a data set. Figure 3 – Sample Variance and Standard Deviation by Column. To calculate the arithmetic mean, sum all t he values and divide by n (equivalently, multiple 1/n): 1. Step 2: Find the third quartile, Q 3. To find the value of mean, divide this sum by the total number of observations in the data. Column A provides the individual values or scores are used to calculate the mean. The test is based on the difference between the first and third quartile of the sample (Q1 and Q3). So this is gonna give us our inter quartile range. The larger the standard deviation, the the individual value are fro. True or False: The line drawn within the box of the boxplot always represents the arithmetic mean. Men's heights have the same shape and parameters 70. Values must be numeric and may be separated by commas, spaces or new-line. The quartiles of a distribution are the three points that divide it into four equally numerous parts. Their mean age was found to be 28 with a standard deviation of 4 years. Mean Average Sx s, s n-1 Sample standard deviation unbiased estimator of the population standard deviation (IB name) x σ, s n Population standard deviation Sample standard deviation (IB name) minX L Minimum value the lowest value Q1 first quartile Med Median Q3 third quartile maxX H Maximum value the highest value Range. In the data set above, the variance is quite high, with only two daily sales totals coming to within \$1,000 of the mean. The first quartile therefore must be 17. So now we wanna select it again. Standard deviation is the square root of the variance.


text:
Outlook: Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities is assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Wait until speculative trend diminishes
Time series to forecast n: 19 Jan 2023 for (n+16 weeks)
Methodology : Inductive Learning (ML)

## Abstract

Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities prediction model is evaluated with Inductive Learning (ML) and ElasticNet Regression1,2,3,4 and it is concluded that the SCE^K stock is predictable in the short/long term. According to price forecasts for (n+16 weeks) period, the dominant strategy among neural network is: Wait until speculative trend diminishes

## Key Points

1. How do you pick a stock?
2. What are the most successful trading algorithms?
3. Game Theory

## SCE^K Target Price Prediction Modeling Methodology

We consider Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities Decision Process with Inductive Learning (ML) where A is the set of discrete actions of SCE^K stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4

F(ElasticNet Regression)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Inductive Learning (ML)) X S(n):→ (n+16 weeks) $\begin{array}{l}\int {e}^{x}\mathrm{rx}\end{array}$

n:Time series to forecast

p:Price signals of SCE^K stock

j:Nash equilibria (Neural Network)

k:Dominated move

a:Best response for target price

For further technical information as per how our model work we invite you to visit the article below:

How do AC Investment Research machine learning (predictive) algorithms actually work?

## SCE^K Stock Forecast (Buy or Sell) for (n+16 weeks)

Sample Set: Neural Network
Stock/Index: SCE^K Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities
Time series to forecast n: 19 Jan 2023 for (n+16 weeks)

According to price forecasts for (n+16 weeks) period, the dominant strategy among neural network is: Wait until speculative trend diminishes

X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)

Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)

Z axis (Grey to Black): *Technical Analysis%

## IFRS Reconciliation Adjustments for Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities

1. When assessing a modified time value of money element, an entity must consider factors that could affect future contractual cash flows. For example, if an entity is assessing a bond with a five-year term and the variable interest rate is reset every six months to a five-year rate, the entity cannot conclude that the contractual cash flows are solely payments of principal and interest on the principal amount outstanding simply because the interest rate curve at the time of the assessment is such that the difference between a five-year interest rate and a six-month interest rate is not significant. Instead, the entity must also consider whether the relationship between the five-year interest rate and the six-month interest rate could change over the life of the instrument such that the contractual (undiscounted) cash flows over the life of the instrument could be significantly different from the (undiscounted) benchmark cash flows. However, an entity must consider only reasonably possible scenarios instead of every possible scenario. If an entity concludes that the contractual (undiscounted) cash flows could be significantly different from the (undiscounted) benchmark cash flows, the financial asset does not meet the condition in paragraphs 4.1.2(b) and 4.1.2A(b) and therefore cannot be measured at amortised cost or fair value through other comprehensive income.
2. If a financial asset contains a contractual term that could change the timing or amount of contractual cash flows (for example, if the asset can be prepaid before maturity or its term can be extended), the entity must determine whether the contractual cash flows that could arise over the life of the instrument due to that contractual term are solely payments of principal and interest on the principal amount outstanding. To make this determination, the entity must assess the contractual cash flows that could arise both before, and after, the change in contractual cash flows. The entity may also need to assess the nature of any contingent event (ie the trigger) that would change the timing or amount of the contractual cash flows. While the nature of the contingent event in itself is not a determinative factor in assessing whether the contractual cash flows are solely payments of principal and interest, it may be an indicator. For example, compare a financial instrument with an interest rate that is reset to a higher rate if the debtor misses a particular number of payments to a financial instrument with an interest rate that is reset to a higher rate if a specified equity index reaches a particular level. It is more likely in the former case that the contractual cash flows over the life of the instrument will be solely payments of principal and interest on the principal amount outstanding because of the relationship between missed payments and an increase in credit risk. (See also paragraph B4.1.18.)
3. If a put option obligation written by an entity or call option right held by an entity prevents a transferred asset from being derecognised and the entity measures the transferred asset at amortised cost, the associated liability is measured at its cost (ie the consideration received) adjusted for the amortisation of any difference between that cost and the gross carrying amount of the transferred asset at the expiration date of the option. For example, assume that the gross carrying amount of the asset on the date of the transfer is CU98 and that the consideration received is CU95. The gross carrying amount of the asset on the option exercise date will be CU100. The initial carrying amount of the associated liability is CU95 and the difference between CU95 and CU100 is recognised in profit or loss using the effective interest method. If the option is exercised, any difference between the carrying amount of the associated liability and the exercise price is recognised in profit or loss.
4. One of the defining characteristics of a derivative is that it has an initial net investment that is smaller than would be required for other types of contracts that would be expected to have a similar response to changes in market factors. An option contract meets that definition because the premium is less than the investment that would be required to obtain the underlying financial instrument to which the option is linked. A currency swap that requires an initial exchange of different currencies of equal fair values meets the definition because it has a zero initial net investment.

*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.

## Conclusions

Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities is assigned short-term Ba1 & long-term Ba1 estimated rating. Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities prediction model is evaluated with Inductive Learning (ML) and ElasticNet Regression1,2,3,4 and it is concluded that the SCE^K stock is predictable in the short/long term. According to price forecasts for (n+16 weeks) period, the dominant strategy among neural network is: Wait until speculative trend diminishes

### SCE^K Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities Financial Analysis*

Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementBa3B2
Balance SheetBaa2Ba3
Leverage RatiosCaa2Baa2
Cash FlowCaa2Caa2
Rates of Return and ProfitabilityB1B1

*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?

### Prediction Confidence Score

Trust metric by Neural Network: 88 out of 100 with 452 signals.

## References

1. Bessler, D. A. R. A. Babula, (1987), "Forecasting wheat exports: Do exchange rates matter?" Journal of Business and Economic Statistics, 5, 397–406.
2. K. Tuyls and G. Weiss. Multiagent learning: Basics, challenges, and prospects. AI Magazine, 33(3): 41–52, 2012
3. Mikolov T, Yih W, Zweig G. 2013c. Linguistic regularities in continuous space word representations. In Pro- ceedings of the 2013 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pp. 746–51. New York: Assoc. Comput. Linguist.
4. Bai J, Ng S. 2017. Principal components and regularized estimation of factor models. arXiv:1708.08137 [stat.ME]
5. E. Altman. Constrained Markov decision processes, volume 7. CRC Press, 1999
6. Wan M, Wang D, Goldman M, Taddy M, Rao J, et al. 2017. Modeling consumer preferences and price sensitiv- ities from large-scale grocery shopping transaction logs. In Proceedings of the 26th International Conference on the World Wide Web, pp. 1103–12. New York: ACM
7. Vilnis L, McCallum A. 2015. Word representations via Gaussian embedding. arXiv:1412.6623 [cs.CL]
Frequently Asked QuestionsQ: What is the prediction methodology for SCE^K stock?
A: SCE^K stock prediction methodology: We evaluate the prediction models Inductive Learning (ML) and ElasticNet Regression
Q: Is SCE^K stock a buy or sell?
A: The dominant strategy among neural network is to Wait until speculative trend diminishes SCE^K Stock.
Q: Is Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities stock a good investment?
A: The consensus rating for Southern California Edison Company 5.45% Fixed-to-Floating Rate Trust Preference Securities is Wait until speculative trend diminishes and is assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of SCE^K stock?
A: The consensus rating for SCE^K is Wait until speculative trend diminishes.
Q: What is the prediction period for SCE^K stock?
A: The prediction period for SCE^K is (n+16 weeks)

## People also ask

What are the top stocks to invest in right now?

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# Quantum Computing #02: Single-qubit gates

## Introduction to Quantum Computing series

Hoa Nguyen

Published on Jun 19, 2021

• Classical example: NOT gate: 0 → 1 ; 1 → 0
• Quantum examples: as quantum theory is unitary, i.e., quantum gates are represented by unitary matrices: $$U^\dagger U = \mathbb{I}$$ (identity matrix)

# The Pauli Gates

$$\sigma_X, \sigma_Y, \sigma_Z$$ are called Pauli matrices and $$\sigma_i^2 = \mathbb{I} = \begin{bmatrix}1 & 0 \ 0&1\end{bmatrix}$$. Apply a same gates 2 times = do nothing! → together with identity $$\mathbb{I}$$, they form a basis of 2x2 matrices

## Pauli-X gate

X-Gate (like classical NOT gate):

$$\sigma_X = X = \begin{bmatrix} 0 & 1 \ 1 & 0 \end{bmatrix} = |0\rangle\langle1| + |1\rangle\langle0|$$

X-gate switches the amplitudes of $$|0\rangle$$ and $$|1\rangle$$

$$X|0\rangle = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\begin{bmatrix} 1 \\ 0 \end{bmatrix} = \begin{bmatrix} 0 \\ 1 \end{bmatrix} = |1\rangle$$

$$X|1\rangle = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix}\begin{bmatrix} 0 \\ 1 \end{bmatrix} = \begin{bmatrix} 1 \\ 0 \end{bmatrix} = |0\rangle$$

$$\Rightarrow$$ a bit flip ~ classical NOT gate (but not only flip bit 0 and 1, but also superposition) → We can think of this as a rotation by $$\pi$$ radians around the x-axis of the Bloch sphere. (→ X-gate would not have any effect on $$|+\rangle$$ and $$|-\rangle$$ state)

## Pauli-Z gate

$$\sigma_Z = Z = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} = |0\rangle\langle0| - |1\rangle\langle1|$$

Apply $$\sigma_Z$$ to $$|+\rangle$$ and $$|-\rangle$$:

$$\sigma_Z|+\rangle = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}.\frac{1}{\sqrt2}\begin{bmatrix}1 \\1 \end{bmatrix} = \frac{1}{\sqrt2}\begin{bmatrix}1 \\-1 \end{bmatrix} = |-\rangle$$

$$\sigma_Z|-\rangle = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}.\frac{1}{\sqrt2}\begin{bmatrix}1 \\-1 \end{bmatrix} = \frac{1}{\sqrt2}\begin{bmatrix}1 \\1 \end{bmatrix} = |+\rangle$$

or $$\sigma_X|-\rangle = (|0\rangle\langle0| - |1\rangle\langle1|).\frac{1}{\sqrt2}(|0\rangle - |1\rangle) = \frac{1}{\sqrt2}(|0\rangle + |1\rangle) = |+\rangle$$

$$\Rightarrow$$ a phase flip (rotation around the z-axis by $$\pi$$)

## Pauli-Y gate

$$\sigma_Y = Y = \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} = -i|0\rangle\langle1| + i|1\rangle\langle0| = i.\sigma_X.\sigma_Z$$

→ rotations by $$\pi$$ around the y-axis of the Bloch sphere $$\Rightarrow$$ bit and phase flip

It allows us to move away from the poles of the Bloch sphere and create a superposition of $$|0\rangle$$ and $$|1\rangle$$:

$$H = \tfrac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} = \tfrac{1}{\sqrt{2}}(|0\rangle\langle0|+|0\rangle\langle1| + |1\rangle\langle0| - |1\rangle\langle1|)$$

$$H|0\rangle = |+\rangle \Rightarrow H|+\rangle = |0\rangle$$

$$H|1\rangle = |-\rangle \Rightarrow H|-\rangle = |1\rangle$$

→ Going back and forth → used to change between X and Z basis.

This can be thought of as a rotation around the Bloch vector [1,0,1] (the line between the x & z-axis), or as transforming the state of the qubit between the X and Z bases.

## The R$$_\phi$$-gate

• The $$R_\phi$$ gate is parametrized, that is, it needs a number $$\phi$$ to tell it exactly what to do.
• The $$R_\phi$$ gate performs a rotation of ϕ around the Z-axis direction (and as such is sometimes also known as the $$R_z$$ gate

$$R_\phi = \begin{bmatrix} 1 & 0 \ 0 & e^{i\phi} \end{bmatrix}$$ where $$\phi$$ is a real number

## The I, S and T-gates

The I, Z, S & T-gates were all special cases of the more general Rϕ-gate

### The I-gate

• The I-gate (aka ‘Id-gate’ or ‘Identity gate’). This is simply a gate that does nothing. Its matrix is the identity matrix:

$$I = \begin{bmatrix} 1 & 0 \\ 0 & 1\end{bmatrix}$$

• Applying the identity gate anywhere in your circuit should have no effect on the qubit state, so it’s interesting this is even considered a gate, because:

1. It is often used in calculations. For example: proving the X-gate is its own inverse: $$I = XX$$
2. it is often useful when considering real hardware to specify a ‘do-nothing’ or ‘none’ operation.

### The S-gate

• S-gate (sometimes known as the $$\sqrt{Z}$$ -gate), this is an $$R_\phi$$ gate with $$\phi = \pi/2$$

$$S = \begin{bmatrix} 1 & 0 \\ 0 & i\end{bmatrix}$$ adds $$\pi/2$$ to the phase $$\phi$$

$$S|+\rangle = |+i\rangle$$ and $$S|-\rangle = |-i\rangle$$

$$\Rightarrow S.H$$ is applied to change from $$Z$$ to $$Y$$ basis

• It does a quarter-turn around the Bloch sphere.

• It is important to note that unlike every gate introduced in this chapter so far, the S-gate is not its own inverse!

$$S^\dagger$$ gate, (also “S-dagger”, “Sdg” or $$\sqrt{Z}^\dagger$$ gate) is $$R_\phi$$ gate with $$\phi = -\pi/2$$

$$S = \begin{bmatrix} 1 & 0 \\ 0 & e^{\frac{i\pi}{2}} \end{bmatrix}, \quad S^\dagger = \begin{bmatrix} 1 & 0 \\ 0 & e^{-\frac{i\pi}{2}} \end{bmatrix}$$

• The name "$$\sqrt{Z}$$-gate" is due to the fact that two successively applied S-gates has the same effect as one Z-gate:

$$SS|q\rangle = Z|q\rangle$$

### The T-gate

• The T-gate is a very commonly used gate, this is an $$R_\phi$$ gate with $$\phi = \pi/4$$:

$$T = \begin{bmatrix} 1 & 0 \\ 0 & e^{\frac{i\pi}{4}} \end{bmatrix}, \quad T^\dagger = \begin{bmatrix} 1 & 0 \\ 0 & e^{-\frac{i\pi}{4}} \end{bmatrix}$$

As with the S-gate, the T-gate is sometimes also known as the $$\sqrt[4]{Z}$$-gate.

## General U-gates

The U_3\)-gate is the most general of all single-qubit quantum gates. It is a parametrized gate of the form

$$U_3(\theta, \phi, \lambda) = \begin{bmatrix} \cos(\theta/2) & -e^{i\lambda}\sin(\theta/2) \\ e^{i\phi}\sin(\theta/2) & e^{i\lambda+i\phi}\cos(\theta/2) \end{bmatrix}$$

Every gate in this chapter could be specified as $$U_3(\theta,\phi,\lambda)$$, but it is unusual to see this in a circuit diagram, possibly due to the difficulty in reading this.

Qiskit provides $$U_2$$ and $$U_1$$ gates, which are specific cases of the $$U_3$$ gate in which $$\theta=\pi/2$$, and $$\theta = \phi = 0$$ respectively.

• U1-gate is equivalent to the Rϕ-gate

\begin{aligned} U_3(\tfrac{\pi}{2}, \phi, \lambda) = U_2 = \tfrac{1}{\sqrt{2}}\begin{bmatrix} 1 & -e^{i\lambda} \\ e^{i\phi} & e^{i\lambda+i\phi} \end{bmatrix} & \quad & U_3(0, 0, \lambda) = U_1 = \begin{bmatrix} 1 & 0 \ 0 & e^{i\lambda}\\ \end{bmatrix} \end{aligned}


text:
Long Multiplication | Grid Method | Maths Made Easy

# Long Multiplication and Grid Method

Level 1-3

## Long Multiplication and Grid Method

The 2 multiplication methods we will see are the long multiplication (column) method and the grid method. The grid method is taught by many schools in the UK but there are many that prefer long multiplication, so we will look at both.

KS3 Level 1-3

## Method 1: Long Multiplication (Column) Method

Step 1: Write the two numbers we are multiplying on top of each other, usually with the bigger one on top. We write the values so that the $1$s, $10$s, $100$s and so on all line up in the correct column.

Step 2: Multiply the last digit from the bottom number with every digit from the top number, writing the results underneath from right to left, and carrying forward when values go above $10$

$3\times1 = 3$, $3\times8=24$, $3\times2 = 6$

Step 3: Next, the second digit is the tens digit, for this we write a $0$ underneath the last step’s working so that everything is shifted one space to the left.

We then multiply this digit by every digit from the top number, writing the results underneath the last step from right to left.

Step 4: Add up the final numbers using the column addition method, writing the results under another line.

From this we can see:

$281 \times 23 = 6463$

KS3 Level 1-3
KS3 Level 1-3

## Method 2: The Grid Method

Step 1: Split each number into $1$s, $10$s, $100$s and so on, and write each component of one number along the top of a grid, and each component of the other number down the left-hand side.

$\textcolor{red}{2}\textcolor{blue}{1}\textcolor{limegreen}{3} \times \textcolor{maroon}{7}\textcolor{purple}{4}$

Step 2: Fill all the squares of the grid by multiplying each part of one number by each part of the other.

$14000+800+700+210+40+12=15762$

KS3 Level 1-3

## Example: The Grid Method

Work out $23\times 281$, without using a calculator.

[3 marks]

Split each number into $1$s, $10$s, $100$s and so on, writing each component of one number along the top of the grid, and each component of the other number down the left-hand side. Then, fill all the squares of the grid by multiplying each bit of one number by each bit of the other number.

Then, by whichever method you prefer, add together all the answers in the grid.

$4000+1600+600+240+20+3=6463$

So,

$281 \times 23 = 6463$

KS3 Level 1-3

## GCSE Maths Revision Cards

(242 Reviews) £8.99

### Example Questions

For this multiplication we will use the long multiplication method, multiplying $619$ first by $5$ then by $40$

$\begin{array}{r}619\\\times45\\\hline3095\\24760\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}3095\\+24760\\\hline27855\end{array}\end{array}$

For this multiplication we will use the long multiplication method, multiplying $52$ first by $1$ then by $30$

$\begin{array}{r}\begin{array}{r}52\\\times31\\\hline52\\1560\end{array}\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}52\\+1560\\\hline1612\end{array}\end{array}$

For this multiplication we will use the long multiplication method, multiplying $760$ first by $4$ then by $20$

$\begin{array}{r}\begin{array}{r}760\\\times24\\\hline3040\\15200\end{array}\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}3040\\+15200\\\hline18240\end{array}\end{array}$

For this multiplication we will use the long multiplication method, multiplying $364$ first by $2$ then by $50$

$\begin{array}{r}\begin{array}{r}364\\\times52\\\hline728\\18200\end{array}\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}728\\+18200\\\hline18928\end{array}\end{array}$

For this multiplication we will use the long multiplication method, multiplying $185$ first by $8$ then by $30$

$\begin{array}{r}\begin{array}{r}185\\\times38\\\hline1480\\5550\end{array}\end{array}$

Adding the results of each components multiplication,

$\begin{array}{r}\begin{array}{r}1480\\+5550\\\hline7030\end{array}\end{array}$

### Worksheets and Exam Questions

#### (NEW) Long Multiplication - Exam Style Questions - MME

Level 1-3 New Official MME

### Learning resources you may be interested in

We have a range of learning resources to compliment our website content perfectly. Check them out below.


text:
# Compact embedding

Prove that the embedding

$j\colon (C^1[0,1],\|\cdot\|)\to(L^1[0,1],\|\cdot\|_{L^1})$

where

$\|f\|=\max\{\|f\|_\infty,\|f'\|_\infty\}$ and $\|f\|_\infty$ denotes the supremum norm,

$\|f\|_{L^1}=\int_0^1|f(t)|dt$,

is compact.

I could prove it with the Arzelà-Ascoli, but I don't know if that theorem only works when you want to prove the compactness of a set $M\subset C(S)$, where $S$ is compact.

Could I use Arzelà-Ascoli? Otherwise, how can I solve the problem?

Yes, you can use Ascoli-Arzelà. Most easily seen here if you factor the map through $L^\infty([0,1], \lVert\,\cdot\,\rVert_{L^\infty})$:
$$C^1([0,1],\lVert\,\cdot\,\rVert) \underbrace{\hookrightarrow}_{\text{compact}} L^\infty([0,1], \lVert\,\cdot\,\rVert_{L^\infty}) \underbrace{\hookrightarrow}_{\text{continuous}} L^1([0,1], \lVert\,\cdot\,\rVert_{L^1}).$$


text:
# Joining Paths makes Another Path

## Theorem

Let $T$ be a topological space.

Let $I \subseteq \R$ be the closed real interval $\closedint 0 1$.

Let $f, g: I \to T$ be paths in $T$ from $a$ to $b$ and from $b$ to $c$ respectively.

Let $h: I \to T$ be the mapping given by:

$\map h x = \begin{cases} \map f {2x} & : x \in \closedint 0 {\dfrac 1 2} \\ \map g {2x - 1} & : x \in \closedint {\dfrac 1 2} 1 \end{cases}$

Then $h$ is a path in $T$.

## Proof

First we see that $h$ is well-defined, because on $\closedint 0 {\dfrac 1 2} \cap \closedint {\dfrac 1 2} 1 = \set{\dfrac 1 2}$ we have $\map f 1 = b = \map g 0$.

Now $\mathbin {h} {\restriction_{\closedint 0 {\frac 1 2}}} \mathop = f \circ k$ where $k: \closedint 0 {\dfrac 1 2} \to \closedint 0 1$ is given by $\map k x = 2x$.

So by Continuity of Composite Mapping, $\mathbin {h} {\restriction_{\closedint 0 {\frac 1 2}}}$ is continuous.

Similarly, $\mathbin {h} {\restriction_{\closedint {\frac 1 2} 1}}$ is continuous.

By Continuity from Union of Restrictions, it follows that $h$ is continuous.

Finally, $\map h 0 = \map f 0 = a$ and $\map h 1 = \map g 1 = c$.

$\blacksquare$


text:
## Laws of the iterated logarithm for the Brownian snake.(English)Zbl 0956.60012

Azéma, J. (ed.) et al., Séminaire de Probabilités XXXIV. Berlin: Springer. Lect. Notes Math. 1729, 302-312 (2000).
Summary: We consider the path-valued process $$(W_s,\zeta_s)$$ called the Brownian snake, with lifetime process $$(\zeta_s)$$ a reflected Brownian motion. We first give an estimate of the probability that this process exits a “big” ball. Then we show the following laws of the iterated logarithm for the Euclidean norm of the “terminal point” of the Brownian snake: $\limsup_{s\uparrow+\infty} {|W_s(\zeta_s)|\over s^{1/4}(\log\log s)^{3/4}}= c,\quad \limsup_{s\downarrow 0} {|W_s(\zeta_s)|\over s^{1/4}(\log\log(1/s))^{3/4}}= c,$ where $$c= 2.3^{-3/4}$$.
For the entire collection see [Zbl 0940.00007].

### MSC:

 60F15 Strong limit theorems 60F10 Large deviations 60G15 Gaussian processes 60G17 Sample path properties 60J25 Continuous-time Markov processes on general state spaces
Full Text:


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# Your average reading speed is 160 words per minute. There are approximately 800 words on each page of the textbook you need to read. Approximately how long will it take you to read 50 pages of your textbook?

Time taken to read the text book is
$4$hours$10$minutes

#### Explanation:

average reading speed $= 160$ words per minute
Number of words per page $= 800$
Time taken to complete each page is
$\frac{800}{160} = 5$minutes
Number of pages in text book$= 50$
Time taken to read the text book is
$= 5 \times 50 = 250$minutes
$= \frac{250}{60} = 4 \times \frac{10}{60}$

$4$hours$10$minutes


text:
# Prove a given sequence of real numbers is convergent

Given the sequence of real numbers $\{x_n\}_{n \in \mathbb N}$, we define $\{y_n\}_{n \in \mathbb N}$ where $y_n=\max\{|x_1|,...,|x_n|\}$ for each $n \in \mathbb N$. Prove that if $\{x_n\}_{n \in \mathbb N}$ is bounded, then $\{y_n\}_{n \in \mathbb N}$ is a convergent sequence.

My attempt at a solution.

If $\{x_n\}_{n \in \mathbb N}$ is bounded, then, it has a convergent subsequence. Call that sequence $\{x_{n_k}\}_{k \in \mathbb N}$. Note that if $x=\lim_{k \to \infty} x_{n_k}$, then $|x|=\lim_{k \to \infty}|x_{n_k}|$. This can be proved by the fact that $0\leq ||x_{n_k}|-|x||\leq |x_{n_k}-x| \to 0$ when $k \to \infty$.

I was going to try to prove that $|x|=lim_{n \to \infty} y_n$ but immediately realize that this doesn't need to be true. For example: $\{x_n\}_{n \in \mathbb N}$: $x_n=0$ if $n$ is odd and $x_n=1$ if $n$ is even has two convergent subsequences.

My problem is I don't know what else to do, I would appreciate some guidance.

-
To show that $y_n$ is convergent, focus on the properties of $y_n$. There are several facts about $y_n$ that you should be able to deduce directly from your above statements. Do those facts help you to prove convergence? – John Dec 20 '13 at 19:40
@John right, $\{y_n\}_{n \in \mathbb N}$ is bounded and it is monotone increasing, I can't believe I didn't realize it before – user100106 Dec 20 '13 at 19:43
@user100106 : the MSE system dislikes unanswered questions. You can answer your own question, or John can answer it. – Stefan Smith Dec 20 '13 at 20:04

To show that $y_n$ is convergent, focus on the properties of $y_n$. There are several facts about $y_n$ that you should be able to deduce directly from your above statements. Do those facts help you to prove convergence?


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# Group query results

Grouping is one of the most powerful capabilities of LINQ. The following examples show how to group data in various ways:

• By a single property.

• By the first letter of a string property.

• By a computed numeric range.

• By Boolean predicate or other expression.

• By a compound key.

In addition, the last two queries project their results into a new anonymous type that contains only the student's first and last name. For more information, see the group clause.

Note

The examples in this topic use the Student class and students list from the sample code in Query a collection of objects.

## Group by single property example

The following example shows how to group source elements by using a single property of the element as the group key. In this case the key is a string, the student's last name. It is also possible to use a substring for the key; see the next example. The grouping operation uses the default equality comparer for the type.

// Variable queryLastNames is an IEnumerable<IGrouping<string,
// DataClass.Student>>.
var groupByLastNamesQuery =
from student in students
group student by student.LastName into newGroup
orderby newGroup.Key
select newGroup;

foreach (var nameGroup in groupByLastNamesQuery)
{
Console.WriteLine($"Key: {nameGroup.Key}"); foreach (var student in nameGroup) { Console.WriteLine($"\t{student.LastName}, {student.FirstName}");
}
}

/* Output:
Key: Fakhouri
Key: Feng
Feng, Hanying
Key: Garcia
Garcia, Cesar
Garcia, Debra
Garcia, Hugo
Key: Mortensen
Mortensen, Sven
Key: O'Donnell
O'Donnell, Claire
Key: Omelchenko
Omelchenko, Svetlana
Key: Tucker
Tucker, Lance
Tucker, Michael
Key: Zabokritski
Zabokritski, Eugene
*/

## Group by value example

The following example shows how to group source elements by using something other than a property of the object for the group key. In this example, the key is the first letter of the student's last name.

var groupByFirstLetterQuery =
from student in students
group student by student.LastName[0];

foreach (var studentGroup in groupByFirstLetterQuery)
{
Console.WriteLine($"Key: {studentGroup.Key}"); // Nested foreach is required to access group items. foreach (var student in studentGroup) { Console.WriteLine($"\t{student.LastName}, {student.FirstName}");
}
}

/* Output:
Key: A
Key: F
Feng, Hanying
Key: G
Garcia, Cesar
Garcia, Debra
Garcia, Hugo
Key: M
Mortensen, Sven
Key: O
O'Donnell, Claire
Omelchenko, Svetlana
Key: T
Tucker, Lance
Tucker, Michael
Key: Z
Zabokritski, Eugene
*/

## Group by a range example

The following example shows how to group source elements by using a numeric range as a group key. The query then projects the results into an anonymous type that contains only the first and last name and the percentile range to which the student belongs. An anonymous type is used because it is not necessary to use the complete Student object to display the results. GetPercentile is a helper function that calculates a percentile based on the student's average score. The method returns an integer between 0 and 10.

int GetPercentile(Student s)
{
double avg = s.ExamScores.Average();
return avg > 0 ? (int)avg / 10 : 0;
}

var groupByPercentileQuery =
from student in students
let percentile = GetPercentile(student)
group new
{
student.FirstName,
student.LastName
} by percentile into percentGroup
orderby percentGroup.Key
select percentGroup;

// Nested foreach required to iterate over groups and group items.
foreach (var studentGroup in groupByPercentileQuery)
{
Console.WriteLine($"Key: {studentGroup.Key * 10}"); foreach (var item in studentGroup) { Console.WriteLine($"\t{item.LastName}, {item.FirstName}");
}
}

/* Output:
Key: 60
Garcia, Debra
Key: 70
O'Donnell, Claire
Key: 80
Feng, Hanying
Garcia, Cesar
Garcia, Hugo
Mortensen, Sven
Omelchenko, Svetlana
Tucker, Lance
Zabokritski, Eugene
Key: 90
Tucker, Michael
*/

## Group by comparison example

The following example shows how to group source elements by using a Boolean comparison expression. In this example, the Boolean expression tests whether a student's average exam score is greater than 75. As in previous examples, the results are projected into an anonymous type because the complete source element is not needed. Note that the properties in the anonymous type become properties on the Key member and can be accessed by name when the query is executed.

var groupByHighAverageQuery =
from student in students
group new
{
student.FirstName,
student.LastName
} by student.ExamScores.Average() > 75 into studentGroup
select studentGroup;

foreach (var studentGroup in groupByHighAverageQuery)
{
Console.WriteLine($"Key: {studentGroup.Key}"); foreach (var student in studentGroup) { Console.WriteLine($"\t{student.FirstName} {student.LastName}");
}
}

/* Output:
Key: True
Hanying Feng
Cesar Garcia
Hugo Garcia
Sven Mortensen
Svetlana Omelchenko
Lance Tucker
Michael Tucker
Eugene Zabokritski
Key: False
Debra Garcia
Claire O'Donnell
*/

## Group by anonymous type

The following example shows how to use an anonymous type to encapsulate a key that contains multiple values. In this example, the first key value is the first letter of the student's last name. The second key value is a Boolean that specifies whether the student scored over 85 on the first exam. You can order the groups by any property in the key.

var groupByCompoundKey =
from student in students
group student by new
{
FirstLetter = student.LastName[0],
IsScoreOver85 = student.ExamScores[0] > 85
} into studentGroup
orderby studentGroup.Key.FirstLetter
select studentGroup;

foreach (var scoreGroup in groupByCompoundKey)
{
string s = scoreGroup.Key.IsScoreOver85 == true ? "more than 85" : "less than 85";
Console.WriteLine($"Name starts with {scoreGroup.Key.FirstLetter} who scored {s}"); foreach (var item in scoreGroup) { Console.WriteLine($"\t{item.FirstName} {item.LastName}");
}
}

/* Output:
Name starts with A who scored more than 85
Name starts with F who scored more than 85
Hanying Feng
Name starts with G who scored more than 85
Cesar Garcia
Hugo Garcia
Name starts with G who scored less than 85
Debra Garcia
Name starts with M who scored more than 85
Sven Mortensen
Name starts with O who scored less than 85
Claire O'Donnell
Name starts with O who scored more than 85
Svetlana Omelchenko
Name starts with T who scored less than 85
Lance Tucker
Name starts with T who scored more than 85
Michael Tucker
Name starts with Z who scored more than 85
Eugene Zabokritski
*/


text:
# Simply connected quasi-projective varieties in positive characteristic

I am looking for examples of non-projective (quasi-projective) varieties $X$ defined over a field of positive characteristic, which have trivial étale fundamental group.

It is well known that the étale fundamental group in positive characteristics is a very difficult object, especially so in the non-projective case due to possibly wild ramification at infinity. I'm not even sure if there are examples of the kind above. Is this known?

-
Note that any projective variety is quasi-projective. A comparison theorem of Grothendieck gives many examples of projective varieties in positive characteristic with trivial etale fundamental group. So probably you wish to amend your question slightly? –  Pete L. Clark Feb 22 '10 at 11:59
I am fairly sure that removing a codimension $2$ subvariety from a projective variety doesn't change the fundamental group. So I can take any projective example of dimension $2$ or greater and make it nonprojective by yanking out a point. –  David Speyer Feb 22 '10 at 12:21
In fact David's comment is SGA1 Corollary X.3.3 and has now reminded me of an old question of mine at mathoverflow.net/questions/5375/… –  Frank Feb 22 '10 at 12:29
@DS: Grothendieck's specialization theorem applies to any projective variety which lifts to characteristic $0$. So for instance $\mathbb{P}^2$ is simply connected in all characteristics. So based on what you say (which I haven't seen before but sounds good to me), $\mathbb{P}^2$ minus a point is an example. –  Pete L. Clark Feb 22 '10 at 12:31
Technical point: I should have asked for the bigger variety to be regular. –  David Speyer Feb 22 '10 at 12:48

This is an answer to Pete's question on simply connected affine varieties (I can not put it in a comment because of space limitation).

I think that in positive characteristic $p$, no affine irreducible variety $X$ of positive dimension is simply connected. We can assume $X=\operatorname{Spec}(A)$ integral because $\pi_1$ is insensible to nipotent elements (SGA IX.4.10). Let $k[t_1,\ldots, t_d] \subseteq A$ be a finite extension with minimal degree $[k(A):k(t_1,\ldots, t_d)]$. Consider the étale cover $Y\to \mathbb A^d_k= \operatorname{Spec}(k[t_1,\ldots, t_d])$ defined by $s^p-s=t_1$. Then $X\times_{\mathbb A^d_k} Y\to X$ is an étale cover of degree $p$. As $k(Y)$ and $k(X)$ are linearly disjoint over $k(t_1,\ldots, t_d)$ ($k(Y)$ is Galois over $k({\bf t}):=k(t_1,\ldots, t_d)$ and $k(Y)\cap k(X)=k({\bf t})$), the tensor product $k(Y)\otimes_{k({\bf t})} k(X)$ is a field. This implies that $X\times_{\mathbb A^d_k} Y$ is connected.

-

Here's a remark. It's a generalisation of a theorem of Katz-Lang given by Szamuely and Spieß that for a quasi-projective variety over a perfect field $k$, the abelianised tame fundamental group sits in the following exact sequence

$0\rightarrow T \rightarrow \pi_1^{t,ab}(X) \rightarrow T(Alb_X)\rightarrow 0$

where $T$ is a group related to the torsion subgroup in the Neron-Severi group $NS(X)$ and $T(Alb_X)$ is the full Tate module of the generalised Albanese variety of $X$. The definition of tame covers tries to control exactly this wild ramification at infinity (i.e control the function field for the points in $\mathfrak{X}\setminus X$ where $\mathfrak{X}$ is the corresponding projective). You can find more in Szamuely's new book for example.

-

It is a direct consequence of Abhyankar's Conjecture (which was proved by Raynaud and Harbater) that if $k$ is an algebraically closed field of characteristic $p > 0$, then no affine curve $X_{/k}$ has trivial etale fundamental group. (Note that for curves, affine = quasi-projective, non-projective, by Riemann-Roch.)

I have some lecture notes on this subject from years back:

http://math.uga.edu/~pete/fundincharp.pdf

(In contrast to what it says on the first page, they are from 2002.)

Addendum: The comments above give plenty of examples of non-projective quasi-projective varieties with trivial etale fundamental group in characteristic $p$ (or really in characteristic quelconque). An interesting question left open by these examples is whether there are any (nontrivial) simply connected affine varieties in characteristic $p$. As I have said, the answer is "no" in dimension one.

-
Regarding the question of finding a simply connected affine variety (of positive dimension): I'm tempted to say that it is not possible. Embed $X$ into $\mathbb{A}^n$ and take a nontrivial cover of $\mathbb{A}^n$ to get a nontrivial cover of $X$. The gap in this argument, of course, is that the cover of $X$ might not be connected. Any idea how to get around this? –  David Speyer Feb 22 '10 at 14:36
If it is an open subset if $\mathbb{A}^n$, then they are birational and you can use extensions of $\mathbb{A}^n$ that introduce a common nontrivial extension of their function fields. –  Tyler Lawson Feb 22 '10 at 14:50
$\mathbb{P}_k^1$, over an algebraically closed field, is such an example. You can adapt the proof that $\mathbb{Q}$ has no unramified extensions to show that $k(t)$ has no unramified extensions.


text:
So far first DD command worked successfully! Even though I could have sworn in all the previous times I had tried doing this, I did infact have the exact number of cylinders for both partitions. Either way I'm happy the first one worked and that makes me feel like the second one is going to work as well!

Oh and I noticed that you had a little typo in your last post where you were giving me the commands, you said "...of=/sdb1" and "of=/sdb2" instead of putting the /dev/ in there. I'm assuming it would shoot back an error at you if you excluded the /dev/ just thought I'd let you know of the minor typo.


text:
# 8. Data Types¶

The modules described in this chapter provide a variety of specialized data types such as dates and times, fixed-type arrays, heap queues, synchronized queues, and sets.

Python also provides some built-in data types, in particular, dict, list, set (which along with frozenset, replaces the deprecated sets module), and tuple. The str class can be used to handle binary data and 8-bit text, and the unicode class to handle Unicode text.

The following modules are documented in this chapter:


text:
# Probability of getting a white ball when white ball is added in urn.

There are $2$ balls in an urn. Each ball is either white or black. If a white ball is put into an urn and thereafter a ball is drawn at random from the urn, then find the probability that it is white.

Does "each ball is either white or black" mean that there are 3 cases, which are

• $2$ black balls

• $2$ white balls

• $1$ black ball and $1$ white ball?

Also if we add one white ball and then find probability for three cases and then add three probabilities , wouldn't probability be greater than 1?

• – Henry Apr 8 '17 at 16:05
• ... and the last of Lewis Carroll's Pillow Problems – Henry Apr 8 '17 at 16:19

As you say, there are three cases, as the original urn has $U$ white balls where $U$ could be $0$, $1$ or $2$. We can calculate the probability the event of drawing a white ball, $W$ in each case. We would write these as $\mathbb P(W\mid U=0)$, $\mathbb P(W\mid U=1)$ and $\mathbb P(W\mid U=2)$. As Edward Porcella says, we have $\mathbb P(W\mid U=0)=1/3$, $\mathbb P(W\mid U=1)=2/3$ and $\mathbb P(W\mid U=2)=1$.
We don't simply add these probabilities. First we have to multiply each probability by the probability of being in that case in the first place. This is because $$\mathbb P(W\mid U=0)\mathbb P(U=0)=\mathbb P(U=0\text{ and }W),$$ and so on, and $$\mathbb P(W)=\mathbb P(U=0\text{ and }W)+\mathbb P(U=1\text{ and }W)+\mathbb P(U=2\text{ and }W).$$
Unfortunately the original problem doesn't tell us what $\mathbb P(U=0)$, etc, are.
The most natural interpretation is that each ball is independently equally likely to be black or white. This gives $\mathbb P(U=0)=\mathbb P(U=2)=1/4$ and $\mathbb P(U=1)=1/2$, and so the answer is $2/3$. Edward Porcella's answer makes the (different) assumption that all three cases are equally likely. This gives the same answer, as in fact does any interpretation where the cases $U=0$ and $U=2$ are equally likely.
The probability is $\frac23$. As you say, after the white ball is added there are one, two, or three white balls in the urn. But the probability of drawing a white ball is not greater than $1$ since only one of the three possibilities is true, and we don't know which. You're either certain to draw a white ball, or have a two-thirds chance, or a one-third chance. The average of $\frac13$,$\frac23$, and $\frac33$ is $\frac23$.


text:
# The volume V of gas varies inversely as the pressure P on it. The volume of a gas is 200 cm^3 under a pressure of 21 kg/cm^2. What will it's volume under a pressure of 30/kg/cm^2?

Oct 27, 2016

140 $c {m}^{2}$

#### Explanation:

Boyle's law states that for a fixed mass of gas at constant temperature, the absolute pressure and the volume of a gas are inversely proportional.
$p 1 \cdot v 1 = p 2 \cdot v 2$

So,
$p 1 \cdot v 1 = p 2 \cdot v 2$
21 kg/$c {m}^{2}$ × 200 $c {m}^{3}$ = 30 kg/$c {m}^{2}$× v2

v2 = 140 $c {m}^{2}$


text: To avoid a sense of entitlement, we need to draw closer to the Savior. #Sketchnotes from Dale G. Renlund in Apr 2016 #LDSConf


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Amalgam

A set $M$ represented as the set-theoretic union of a family $\{ {A _ {i} } : {i \in I } \}$ of algebraic systems (cf. Algebraic system) $A _ {i}$ of a given class $\mathfrak K$ with intersections $U _ {ij}$, where for all $i, j$ the intersection

$$A _ {i} \cap A _ {j} = U _ {i j } = U _ {j i }$$

is non-empty and is a subsystem of each of the systems $A _ {i} , A _ {j}$. If there exists a system $B$ in the class $\mathfrak K$ containing all $A _ {i}$( $i \in I$) as subsystems, then says one that the amalgam is imbeddable in the system $B$.

An amalgam of two groups and, in general, any amalgam of groups $\{ {A _ {i} } : {i \in I } \}$, in which all intersections $U _ {ij}$( $i \neq j$) coincide and are equal to $U$, is always imbeddable in a group, e.g. in the free product of the groups $A _ {i}$( $i \in I$) with the common subgroup $U$. There are, however, amalgams of groups which are not imbeddable in a group. (For conditions for imbeddability of amalgams of groups in a group see [1]; for imbeddability of amalgams of semi-groups in a semi-group see [2]). See also Amalgam of groups.

Let $\mathfrak K$ be the class of all algebras over a given field $F$ or the class of commutative, anti-commutative or Lie algebras over a field $F$. An amalgam $\{ {A _ {i} } : {i \in I } \}$ of $\mathfrak K$- algebras $A _ {i}$ with identical intersections $U _ {ij} = U$( for all $i \neq j$) is imbeddable in the $\mathfrak K$- free product of these algebras with the common subalgebra $U$[3]. It has been shown [4] that an amalgam $\{ {T _ {i} } : {i \in I } \}$ of associative skew-fields $T _ {i}$ with identical intersections $T _ {ij} = T$( $i \neq j$) is imbeddable in an associative skew-field.

References

 [1] A.G. Kurosh, "The theory of groups" , 2 , Chelsea (1960) pp. 33 (Translated from Russian) [2] A.H. Clifford, G.B. Preston, "Algebraic theory of semi-groups" , 2 , Amer. Math. Soc. (1967) [3] A.I. Shirshov, "On a hypothesis in the theory of Lie algebras" Sibirsk. Mat. Zh. , 3 : 2 (1962) pp. 297–301 (In Russian) [4] P.M. Cohn, "The embedding of firs in skew fields" Proc. London Math. Soc. (3) , 23 (1971) pp. 193–213


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# PSEB 4th Class Maths Solutions Chapter 7 Shapes Ex 7.1

Punjab State Board PSEB 4th Class Maths Book Solutions Chapter 7 Shapes Ex 7.1 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 4 Maths Chapter 7 Shapes Ex 7.1

Question 1.
From the given figure write the names of the following :
(b) diameter
(c) chords

Solution:
(a) Radius = OC, OB, OG, OD, OE, OA
(b) Diameter = AB,EG .
(c) Chords = AF, AB, EG.

Question 2.
Find the radius of a circle whose diameter is :
(a) 6 cm
(b) 8.2 cm
(c) 8.6 cm
Solution:
(a) Diameter of the circle = 6 cm

= $$\frac{6}{2}$$ cm = 3 cm

(b) Diameter of the circle = 8.2 cm

= $$\frac{8.2}{2}$$ cm = 4.1 cm

(c) Diameter of the circle = 8.6 cm

= $$\frac{8.6}{2}$$ cm = 4.3 cm

Question 3.
Find the diameter of a circle whose radius is :
(a) 13 cm
(b) 21 cm
(c) 17 cm
(d) 8 cm
Solution:
(a) Radius of the circle = 13 cm
Diameter of the circle = 2 × Radius
= 2 × 13 cm = 26 cm
(b) Radius of the circle = 21 cm
Diameter of the circle = 2 × Radius
= 2 × 21 cm
= 42 cm
(c) Radius of thte circle = 17 cm
Diameter of the circle = 2 × Radius
= 2 × 17 cm
= 34 cm
(d) Radius of the circle = 8 cm
Diameter of the circle = 2 × Radius
= 2 × 8 cm
= 16 cm

Question 4.
With the help of a compass draw a circle whose radius is :
(a) 5 cm
(b) 3 cm
(c) 2 cm
(d) 3.5 cm
(e) 4.6 cm
(f) 2.5 cm
Solution:

Question 5.
Which is the longest chord of a circle ?
Solution:
Diameter.

Question 6.
Fill in the blanks :
(a) A line segment which joins centre of a circle with any point on circumference is called …………
(b) Diameter of a circle = ………. × radius.
(c) The longest chord of a circle is called …….. of circle.
(d) All the radii of circle are …… in length.
Solution:
(b) 2
(c) Diameter
(d) Equal

Question 7.
Fill the blank

Solution: