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Fix What Is A High Standard Error Value Tutorial

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What Is A High Standard Error Value

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or, to the extent to which it meets the "Magic" criteria, as introduced by Robert Abelson in his book Statistics as Principled Argument (link goes to my review of the book). The formula, (1-P) (most often P < 0.05) is the probability that the population mean will fall in the calculated interval (usually 95%). The smaller the standard error, the less the spread and the more likely it is that any sample mean is close to the population mean. However, different samples drawn from that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and his comment is here

For example, a correlation of 0.01 will be statistically significant for any sample size greater than 1500. Available at: http://damidmlane.com/hyperstat/A103397.html. Suppose the sample size is 1,500 and the significance of the regression is 0.001. Because the 9,732 runners are the entire population, 33.88 years is the population mean, μ {\displaystyle \mu } , and 9.27 years is the population standard deviation, σ. http://www.biochemia-medica.com/content/standard-error-meaning-and-interpretation

How To Interpret Standard Error In Regression

For the same reasons, researchers cannot draw many samples from the population of interest. Another use of the value, 1.96 ± SEM is to determine whether the population parameter is zero. Thanks for writing! The standard deviation is used to help determine validity of the data based the number of data points displayed within each level of standard deviation.

1. mean, or more simply as SEM.
2. What commercial flight route requires the most stops/layovers from A to B?
3. In theory, the coefficient of a given independent variable is its proportional effect on the average value of the dependent variable, others things being equal.
4. The survey with the lower relative standard error can be said to have a more precise measurement, since it has proportionately less sampling variation around the mean.
5. R-squared is not the bottom line.
6. However, one is left with the question of how accurate are predictions based on the regression?
7. Large S.E.

The smaller the standard error, the closer the sample statistic is to the population parameter. Sometimes the inclusion or exclusion of a few unusual observations can make a big a difference in the comparative statistics of different models. Sampling from a distribution with a large standard deviation The first data set consists of the ages of 9,732 women who completed the 2012 Cherry Blossom run, a 10-mile race held Standard Error Example The two concepts would appear to be very similar.

S represents the average distance that the observed values fall from the regression line. Estimates with a RSE of 25% or greater are subject to high sampling error and should be used with caution. Standard error. http://www.biochemia-medica.com/content/standard-error-meaning-and-interpretation Coefficient of determination   The great value of the coefficient of determination is that through use of the Pearson R statistic and the standard error of the estimate, the researcher can

For an upcoming national election, 2000 voters are chosen at random and asked if they will vote for candidate A or candidate B. Standard Error Of Estimate Calculator How to report trailhead bugs Trick or Treat polyglot Interlace strings Why did my cron job run this month? Because the age of the runners have a larger standard deviation (9.27 years) than does the age at first marriage (4.72 years), the standard error of the mean is larger for Why does Wolfram Alpha say the roots of a cubic involve square roots of negative numbers, when all three roots are real?

What Is The Standard Error Of The Estimate

How do XMP files encode aperture? The 9% value is the statistic called the coefficient of determination. How To Interpret Standard Error In Regression The following expressions can be used to calculate the upper and lower 95% confidence limits, where x ¯ {\displaystyle {\bar {x}}} is equal to the sample mean, S E {\displaystyle SE} The Standard Error Of The Estimate Is A Measure Of Quizlet In fact, even with non-parametric correlation coefficients (i.e., effect size statistics), a rough estimate of the interval in which the population effect size will fall can be estimated through the same

Available at: http://www.scc.upenn.edu/čAllison4.html. this content The standard error of the mean permits the researcher to construct a confidence interval in which the population mean is likely to fall. Consider, for example, a regression. There's no need to treat questions like these as missing data problems :) –Macro Jan 9 '13 at 13:58 | show 1 more comment Your Answer draft saved draft discarded Standard Error Of Regression Coefficient

The SEM, like the standard deviation, is multiplied by 1.96 to obtain an estimate of where 95% of the population sample means are expected to fall in the theoretical sampling distribution. This is important because the concept of sampling distributions forms the theoretical foundation for the mathematics that allows researchers to draw inferences about populations from samples. Another use of the value, 1.96 ± SEM is to determine whether the population parameter is zero. weblink Statistical Notes.

When the statistic calculated involves two or more variables (such as regression, the t-test) there is another statistic that may be used to determine the importance of the finding. Can Standard Error Be Greater Than 1 When effect sizes (measured as correlation statistics) are relatively small but statistically significant, the standard error is a valuable tool for determining whether that significance is due to good prediction, or The true standard error of the mean, using σ = 9.27, is σ x ¯   = σ n = 9.27 16 = 2.32 {\displaystyle \sigma _{\bar {x}}\ ={\frac {\sigma }{\sqrt

The Minitab Blog Data Analysis Quality Improvement Project Tools Minitab.com Regression Analysis Regression Analysis: How to Interpret S, the Standard Error of the Regression Jim Frost 23 January, 2014

The sample mean x ¯ {\displaystyle {\bar {x}}} = 37.25 is greater than the true population mean μ {\displaystyle \mu } = 33.88 years. But if it is assumed that everything is OK, what information can you obtain from that table? A good rule of thumb is a maximum of one term for every 10 data points. For A Given Set Of Explanatory Variables, In General: Student approximation when σ value is unknown Further information: Student's t-distribution §Confidence intervals In many practical applications, the true value of σ is unknown.

v t e Statistics Outline Index Descriptive statistics Continuous data Center Mean arithmetic geometric harmonic Median Mode Dispersion Variance Standard deviation Coefficient of variation Percentile Range Interquartile range Shape Moments Similarly, the sample standard deviation will very rarely be equal to the population standard deviation. I did ask around Minitab to see what currently used textbooks would be recommended. check over here This gives 9.27/sqrt(16) = 2.32.

It is useful to compare the standard error of the mean for the age of the runners versus the age at first marriage, as in the graph. I was looking for something that would make my fundamentals crystal clear. price, part 3: transformations of variables · Beer sales vs. The standard deviation of all possible sample means is the standard error, and is represented by the symbol σ x ¯ {\displaystyle \sigma _{\bar {x}}} .

Approximately 95% of the observations should fall within plus/minus 2*standard error of the regression from the regression line, which is also a quick approximation of a 95% prediction interval. The mean age for the 16 runners in this particular sample is 37.25. The two most commonly used standard error statistics are the standard error of the mean and the standard error of the estimate. For example, a correlation of 0.01 will be statistically significant for any sample size greater than 1500.

They are quite similar, but are used differently. It represents the standard deviation of the mean within a dataset. Of course, T / n {\displaystyle T/n} is the sample mean x ¯ {\displaystyle {\bar {x}}} . Applied Regression Analysis: How to Present and Use the Results to Avoid Costly Mistakes, part 2 Regression Analysis Tutorial and Examples Comments Name: Mukundraj • Thursday, April 3, 2014 How to

In business and weapons-making, this is often called "bang for the buck". In other words, it is the standard deviation of the sampling distribution of the sample statistic. And that means that the statistic has little accuracy because it is not a good estimate of the population parameter. and Keeping, E.S. (1963) Mathematics of Statistics, van Nostrand, p. 187 ^ Zwillinger D. (1995), Standard Mathematical Tables and Formulae, Chapman&Hall/CRC.


text: Big Night Lyrics, Find out about its chemical and physical properties, states, energy, electrons, oxidation and more. Houses For Sale Vancouver, Rubidium-85 is the dominant form, accounting for 72 per cent of the total, while most of the remainder is the radioactive rubidium-87, which has a … The subshells have a distinct shape and configuration, in which the electrons move freely. Orbital diagrams are pictorial representations of the electron configuration, showing the individual orbitals and the pairing arrangement of .. Join Yahoo Answers and get 100 points today. Rubidium has several applications to the field of medicine. Unsw Adfa, strontium. Money Control, Eye On Juliet Review, 6789 Quail Hill Pkwy, Suite 211 Irvine CA 92603. The fine structure of the energy states is illustrated in Fig. Strontium. COASTAL ENGINEERING RELATED CENTERS FOR OCEANOGRAPHY & MARINE. Find out about its chemical and physical properties, states, energy, electrons, oxidation and more. Britain's Got Talent Season 9 Winner, Rubidium, complete electron configuration. endstream endobj startxref There are 118 elements in the periodic table. The ionisation energies of rubidium are given below. Your email address will not be published. Ole Miss Cross Country Roster, There may not be enough electrons to complete the last orbital for example in Pb. Lilya 4-ever, Zkušenosti s látkou z níž je složen okolní svět ukazují, že většina látek je časově poměrně stálá a mění se jen v delších časových měřítcích. The equation is:1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p<7s<5f<6d<7p. Nottingham University Accommodation Room Types, We'll assume you're ok with this, but you can opt-out if you wish. 1. The 1s orbital at the bottom of the diagram is the orbital with electrons of lowest energy. This website uses cookies to improve your experience. The electronic configuration of each element is decided by the Aufbau principle which states that the electrons fill orbitals in order of increasing energy levels. Dust Storm Alert, ", ground state electron configuration of ground state gaseous neutral rubidium is, Chemical Rubber Company handbook of chemistry and physics. Start with 1s2 and fill until you've depleted all of the electrons. h�bbdb`��3AD��� L�A�i!R2�J\ ���_@� Steel yourself emotionally for colder weather, Jon Bon Jovi: I'm the 'poster boy' for white privilege, Dungy: Dak injury may be a 'blessing in disguise', Fauci: Trump ad takes my words out of context, 'The Wanted' singer reveals he has terminal brain tumor. Is consuming too much alkaline dangerous? Ununennium, also known as eka-francium or simply element , is the hypothetical chemical element with symbol Uue and atomic number Ununennium and Uue are the temporary systematic IUPAC name and symbol respectively, until a permanent name is decided upon. In addition to listing the principle quantum number, n, and the subshell, $$\ell$$, the orbital diagram shows all the different orientations and the spin of every electron. Get your answers by asking now. You can reference the WebElements periodic table as follows:"WebElements, https://www.webelements.com, accessed October 2020. The following are "Clementi-Raimondi" effective nuclear charges, Zeff. Meaning Of Nana In Arabic, Required fields are marked *. 3201 mL = cm³? We hope you are enjoying ScienceStruck! The element has two naturally occurring isotopes. Rubidium atoms have 37 electrons and the shell structure is  2.8.18.8.1. what is the complete electron configuration of rubidium? The ground state electron configuration of ground state gaseous neutral rubidium is [ … This model has been widely accepted, and according to it, each atom has shells, which further have subshells. Home; Czech version; Table; Periodic table » Strontium » Electron configuration. New Wave Amsterdam, Huron Consulting Reviews, In an orbital (box) diagram a box represents each notation and an orbital diagram. Rubidium (Rb) is a silvery-white soft metal of group 1 in the periodic table of elements, with properties similar to alkali metals. Seminole Native Religion, The 1s orbital at the bottom of the diagram is the orbital with electrons of lowest energy. Rubidium atoms have 37 electrons and the shell structure is 2.8.18.8.1. Shipyards Night Market Dogs, The equation is: 1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p<7s<5f<6d<7p. %PDF-1.5 %���� %%EOF Rubidium (Rb) has an atomic mass of 37. Astronomy, science that encompasses the study of all extraterrestrial objects and phenomena. ½. Many times it is necessary to see all the quantum numbers in an electron configuration, this the purpose of the orbital diagram. These cookies do not store any personal information. }=���ԃc-�U7 �60U�.�q�ԍG���,��r\;֚����� ��:-@4[G�F�DGSGcGG��FG�EGق . Each shell and subshell have a limitation on the amount of electrons that it can carry. Each shell has subshells that are named for the type of emission lines produced from different states of angular momentum. Street Legal Rangiora, What is the correct representation for the subshell with n = 2 and l = 1. what is the molarity of a 200.0mL solution containing 5.00g sodium hydroxide? Fill in the orbital energy diagram for the nitride ion using the following key: u = electron with spin "up", d = electron with spin "down", WebElements: THE periodic table on the WWW [www.webelements.com] For example, iron: [Ar] 4s2 3d6: 18 + 2 + 6 = 26 electrons. This table gives a comprehensive list of the electron distribution in all elements. Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. Live Leitrim Gaa Ie, Rubidium Electron Configuration. Nirv Bible Problems, No 1 Party Anthem Lyrics Meaning, lithium 1s2 2s1 (3 electrons) oxygen 1s2 2s2 2p4 (8 electrons) calcium 1s2 2s2 2p6 3s2 3p6 4s2 (20 electrons) titanium 1s2 2s2 2p6 3s2 3p6 4s2 3d2 (22 electrons) rubidium 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s1 (37 electrons) lead 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f14 5d10 6p2 (82 electrons) erbium 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 5s2 4d10 5p6 6s2 4f12 (68 electrons) and the abbreviated ground state electron configurations for these.... helium same as ground state: 1s2 (no abbreviated ground state ec for this element) nitrogen [He] 2s2 2p3 chlorine [Ne] 3s2 3p5 iron [Ar] 4s2 3d6 zinc [Ar] 4s2 3d10 barium [Xe] 6s2 polonium [Xe] 6s2 4f14 5d10 6p4 to check: count the number of electrons each noble gas gives and add it to the superscripts in the rest of the electron configuration. partial orbital diagram: 4s: UP/DOWN 3d1: UP/DOWN 3d2: UP/DOWN 3d3: UP 3d4: UP 3d5: UP (b) Rb (Z = 37) electron configuration: 1s2 2s2. It will also help comprehend the chemical nature and molecular interactions of the elements. Lv 4. 0 0. chalis913. It involves the specific arrangement of electrons in shells and sub-shells of Bohr’s atomic model. Yes, really. Periodic Table of the Elements Electron configuration of Strontium. Horse Events 2020, Diagram of the nuclear composition, electron configuration, chemical data, and valence orbitals of an atom of strontium (atomic number: 38), the most. Understanding it will help in gaining a better understanding of the concept of quantum numbers and their applications in physics and chemistry. They stand for sharp (S), principal (P), diffuse (D), and fundamental (F). 2738 0 obj <> endobj Native American Shadow Walker, IMPORTANT CALENDAR DATES SCHOOL YEAR 2020-21, SCHOOL TERM AND HOLIDAY DATES 2019 – 2020, SCHOOL TERM AND HOLIDAY DATES 2020 – 2021, EXAM INFO & RESULTS /DfE PERFORMANCE TABLES, Castles Of Burgundy 20th Anniversary Insert, Nottingham University Accommodation Room Types. However, the K⁺ ion has one fewer electron (due to its positive charge), so the highest-energy electron must be removed from K to create K⁺, meaning its electron configuration will be 1s²2s²2p⁶3s²3p⁶. Each element has a unique atomic structure that is influenced by its electronic configuration, which is the distribution of electrons across different orbitals of an atom. Which of these elements has an electron configuration of [Kr]5s2? Copyright © Science Struck & Buzzle.com, Inc. What was A.J. Out of these cookies, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. Your email address will not be published. The 1s orbital at the bottom of the diagram is the orbital with electrons of lowest energy. Copyright 1993-2020 Mark Winter [ The University of Sheffield and WebElements Ltd, UK]. An element that conducts thermal energy well and is malleable is? A representation of the atomic spectrum of rubidium. Willow Stream Spa Calgary, Full electron configuration of strontium: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 5s 2. rubidium ← strontium → yttrium Discover the activities, projects, and degrees that will fuel your love of science. The electron configuration of K is 1s²2s²2p⁶3s²3p⁶4s¹. These cookies do not store any personal information. Dekalb County Il Obituaries, Necessary cookies are absolutely essential for the website to function properly. Top 100 Board Games Of All Time, The electron affinity of rubidium is 46.9 kJ mol‑1. Electron orbitals are differently-shaped regions around an atom's nucleus where electrons are mathematically likely to be located. Rb has 37 Electrons. Electronic configuration: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 5s 1 >> Back to key information about the elementBack to key information about the element endstream endobj 2739 0 obj <>/Metadata 95 0 R/Outlines 113 0 R/PageLayout/OneColumn/Pages 2732 0 R/StructTreeRoot 118 0 R/Type/Catalog>> endobj 2740 0 obj <>/Font<>>>/Rotate 0/StructParents 0/Type/Page>> endobj 2741 0 obj <>stream If 4.50 g of the unknown compound contained 0.150 mol of C and 0.300 mol of H, how many moles of oxygen, O, were in the sample? . Honeywell Thermostat Th6220d1002 Wiring Diagram, Simplicity With Kohler Engine Model Cv15s Wiring Diagram, Wiring Diagram Intimidator Utv Turn Signal, Midwest 50 Amp Spa Disconnect Panel Wiring Diagram. The electronic configuration of Rubidium is [Kr] 5s1.

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# README for Karnickel - AST Macros for Python

"it's no ordinary rabbit..."

## What is it?

Karnickel is a small library that allows you to use macros (similar to those found in Lisp) in Python code. In a nutshell, macros allow you to insert code (the macro definition) at a different point in the code (the macro call). It is different from calling functions in that the code is inserted before it is even compiled.

("Karnickel" is German for "rabbit", and there's a vicious killer rabbit in "Monty Python and the Holy Grail" that is best left alone...)

## Using

Use Python 2.6+. You can put macros in any module. Macro definitions are Python functions, like this:

from karnickel import macro

@macro
def macroname(arg1, arg2):
... macro contents ...

Optional arguments are not supported.

If the contents are a single expression (no return), the macro is an expression macro. Otherwise, it is a block macro. If it contains a statement consisting of only __body__, it is a block macro with body.

For using the macros, you must install the import hook:

import karnickel
karnickel.install_hook()

Then, you can import modules that use macros like this:

from module.__macros__ import macro1, macro2

That is, append .__macros__ to the name of the module that contains the macros. Only from-imports are supported.

Usage depends on the macro type:

• Expression macros can be used everywhere as expressions. Arguments are put into the places of macro arguments.

• Block macros without body can only be used as an expression statement -- i.e.:

macroname(arg1, arg2)

• Block macros with body must be used with a with statement:

with macroname(arg1, arg2):
body

Arguments are put into the places of macro arguments, and the body is put into the place of __body__ in the macro definition.

Proper docs may follow as soon as I can find a decent documentation tool.

## Why?

Why not? Seriously, this is a demonstration of what you can do with the Python AST, especially the standard ast module, and import hooks. Besides, it's been fun.

## Installing

Use setup.py:

sudo python setup.py install

## Author

Georg Brandl <georg@python.org>


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# NCERT Exemplar Class 7 Maths Chapter 3 Data Handling

In this chapter, we provide NCERT Exemplar Problems Solutions for Class 7 Maths Chapter 3 Data Handling for English medium students, Which will very helpful for every student in their exams. Students can download the latest NCERT Exemplar Problems Solutions for Class 7 Maths Chapter 3 Data Handling pdf, free NCERT Exemplar Problems Solutions for Class 7 Maths Chapter 3 Data Handling book pdf download. Now you will get step by step solution to each question.

## NCERT Exemplar Class 7 Maths Chapter 3 Data Handling Solutions

Multiple Choice Questions (MCQs)

Question 1:

Solution:

Question 2:
The number of trees in different parks of a city are 33, 38, 48, 33, 34, 34, 33 and 24. The mode of this data is
(a) 24
(b) 34
(c) 33
(d) 48
Solution:
(c) We have, 33, 38, 48, 33, 34, 34, 33 and 24.
On arranging the data in ascending order, we get 24, 33, 33, 33, 34, 34, 38 and 48.
Here, 33 occurs more frequently, i.e. 3 times.
Mode of data = 33
Note Mode is the observation that occurs most frequently in the data.

Question 3:

Which measures of central tendency get affected, if the extreme observations on both the ends of a data arranged in descending order are removed?
(a) Mean and mode                                      (b) Mean and median
(c) Mode and median                                    (d) Mean, median and mode

Solution:

So, if we remove the extrema values that both sum and total number of observations will change. Hence, mean wiii aiso change.
Mode is that observation which occurs the most. So, if extreme value of those values which occurs mostly than mode can affect it they are removed.
Median is the mid value. So, if extreme values are removed than the mid value remains same. Hence, median will not change.

Question 4:
The range of the data 21, 6, 17, 18, 12, 8, 4, 13 is
(a) 17                         (b) 12                         (c) 8                          (d) 15
Solution:
(a) Here,
Highest observation = 21
Lowest observation = 4
Range = Highest observation – Lowest observation
= 21-4 = 17

Question 5:
The median of the data 3, 4, 5, 6, 7, 3, 4 is
(a) 5                           (b) 3                           (c)4                           (d)6
Solution:
(c) We know that, median is the middle most observation.
For finding the median of the data firstly, we arrange the data in ascending order, i.e. Ascending order
i.e 3, 3, 4, 4, 5, 6, 7.
n = 7 (odd)

Question 6:
Out of 5 brands of chocolates in a shop, a boy has to purchase the brand which is most liked by children. What measure of central tendency would be most appropriate, if the data is provided to him?
(a) Mean                    (b) Mode                     (c) Median                 (d) Any of the three
Solution:
(b) Mode is the most appropriate central tendency because it is the observation that occurs most frequently.
Here, by the measurement of mode, we can find out the chocolates which is most liked by children.

Question 7:
There are 2 aces in each of the given set of cards placed face down. From which set are you certain to pick the two aces in the first go?

Solution:
(c) From third set, we are certain to pick the two aces in the first go because it has only 2 cards and it is given that every set has 2 aces.

Question 8:
In the previous question, what is the probability of picking up an ace from set (d)?

Solution:

Question 9:
The difference between the highest and the lowest observations in a data is its
(a) frequency
(b) width
(c) range
(d) mode
Solution:
(c) The difference between the highest and the lowest observations in a data is its range.

Question 10:
In a school, only 2 out of 5 students can participate in a quiz. What is the chance that a student picked at random makes it to the competition?
(a) 20%
(b) 40%
(c) 50%
(d) 30%
Solution:
(b) Total number of outcomes = Total number of students = 5
Number of possible outcomes = Students participating in a quiz = 2

Question 11:
Some integers are marked on a board. What is the range of these integers?

Solution:
(b) Here, highest observation = + 20 and lowest observation = -17
As we know,
Range = Highest observation – Lowest observation = + 20 – (-17)=20 + 17 = 37

Question 12:
On tossing a coin, the outcome is
(b) only tail
Solution:
(d) When we toss a coin, two outcomes are possible, i.e. head or tail.

Question 13:
The mean of three numbers is 40. All the three numbers are different natural numbers. If lowest is 19, what could be highest possible number of remaining two numbers?
(a) 81
(b) 40
(c) 100
(d) 71
Solution:

Question 14:
Khilona earned scores of 97, 73 and 88 respectively in her first three examinations. If she scored 80 in the fourth examination, then her average score will be
(a) increased by 1
(b) increased by 1.5
(c) decreased by 1
(d) decreased by 1.5
Solution:

Question 15:
Which measure of central tendency best represents the data of the most popular politician after a debate?
(a) Mean
(b) Median
(c) Mode
(d) None of these
Solution:
(c) Mode is the most frequent observation in a data. So, the measure of central tendency best represents the data of most popular politician after a debate.

Question 16:
Which of the following has the same mean, median and mode?
(a) 6, 2, 5, 4, 3, 4, 1                                      (b) 4, 2, 2, 1, 3, 2, 3
(c) 2, 3, 7, 3, 8, 3, 2                                       (d) 4, 3, 4, 3, 4, 6, 4
Solution:

Fill in the Blanks
In questions 17 to 31, fill in the blanks to make the statements true.

Question 17:
The difference between the highest and the lowest observations of a data is called _____.
Solution:
The difference between the highest and the lowest observations of a data is called range.

Question 18:
The mean of a data is defined as__________.
Solution:

Question 19:
In a set of observations, the observation that occurs the most often is called__________.
Solution:
Mode is the most often occurring observation in a set of data.

Question 20:
In a given data, arranged in ascending or descending order, the middle most observation is called__________.
Solution:
Median is the value of middle most observation of a given data, which arranged in ascending or descending order.

Question 21:
Mean, median and mode are the measures of __________.
Solution:
Mean, median and mode are the measures of central tendency.

Question 22:
The probability of an event which is certain to happen is __________.
Solution:
The probability of an event which is certain to happen is 1. In other words, probability of a sure event is 1.

Question 23:
The probability of an event which is impossible to happen is  __________.
Solution:
Probability of an impossible event is 0. As impossible events are those which cannot happen.

Question 24:
When a die is thrown, the probability of getting a number less than 7, is __________.
Solution:
When we throw a die, 6 outcomes are possible, i.e. 1,2, 3, 4, 5, 6.
Total outcomes = 6

Question 25:
In throwing a die, the number of possible outcomes is_________.
Solution:
When we throw a die, 6 outcomes are possible. They are 1,2, 3, 4, 5 and 6.

Question 26:
______ can be used to compare two collections of data.
Solution:
A double bar graph can be used to compare two collections of data.

Question 27:
The representation of data with bars of uniform width is called _________.
Solution:
The representation of data with bars of uniform width is called bar graph.

Question 28:If the arithmetic mean of 8, 4, x, 6, 2, 7 is 5, then the value of x is _____.
Solution:

Question 29:
The median of any data lies between the ______ add ___________ observations.
Solution:
The median of any data lies between the minimum add maximum observations.

Question 30:
Median is one of the observations in the data, if number of observations is ____.
Solution:

Question 31:

Solution:

∴ To make the probability highest, we have to take the interval where number of students, i.e. possible outcomes are highest.
Here, probability is highest whose weight is in the interval

True/False

In questions 32 to 49, state whether the statements are True or False.

Question 32:
If a die is thrown, the probability of getting a number greater than 6 is 1.
Solution:
False
As we know, a die has six numbers on it, i.e. 1 to 6. So, it is impossible to get a number greater than 6. Hence, if a die is thrown, the probability of getting a number greater than 6 is 0.

Question 33:
When a coin is tossed, there are 2 possible outcomes.
Solution:
True
If a coin is tossed, then
Maximum outcomes = 2, i.e. head or tail.

Question 34:
If the extreme observations of both the ends of a data arranged in ascending order are removed, the median gets affected.
Solution:
False
If the extreme observations on both the ends of a data arranged in ascending order are removed, then the mean and mode gets affected but median remains same.

Question 35:
The measures of central tendency may not lie between the maximum and minimum values of data.
Solution:
False
The measures of central tendency lie between the maximum and minimum values of the data.

Question 36:
It is impossible to get a sum of 14 of the numbers on both die, when a pair of dice is thrown together.
Solution:
True
When a die is thrown, maximum possible outcomes are 6, i.e. 1,2, 3,4, 5, 6.
So, when a pair of dice is thrown together, maximum sum will be 12, if and only if both dice get 6 together. So, that pair will be (6, 6) and the sum is 12.
∴ It is impossible to get a sum of 14 on both dice, when a pair of dice is thrown together.

Question 37:
The probability of the spinning arrow stopping in the shaded region in the given figure is ½.

Solution:
True
Favourable outcomes = Number of shaded regions = 2
Total number of possible outcomes = Total number of regions = 4

Question 38:
A coin is tossed 15 times and the outcomes are recorded as follows:
H T T H T H H H T T H T H T T
The chance of occurrence of a head is 50 %.
Solution:
False
Number of times in which head occurs = 7
Total number of times, the coin is tossed = 15
∴ Probability of getting a head = $frac{7}{15}$

Question 39:
Mean, median and mode may be the same for some data.
Solution:
TrueMean, median and mode can be the same for some data
See Q. No. 16.

Question 40:
The probability of getting an ace out of a deck of cards is greater than 1.
Solution:
False
Probability of an event can never be greater than 1. It always remains from 0 and 1 for any event.

Question 41:
Mode of the data is always from the given data.
Solution:
FalseIt is not compulsory that mean of the data is always from the given data. It may or may not be the observation from given data.

Question 42:
Median of the data may or may not be from the given data.
Solution:
True

Question 43:
Mode of thedata is always from the given data.
Solution:
True
Mode of the data is always from the given data as it is the most frequent observation in the data.

Question 44:
Mean of the observations can be lesser than each of the observations.
Solution:
False
Mean is the average value of all the observations. Some of the observations are less than it and some of observations are more than it.

Question 45:
Mean can never be a fraction.
Solution:
False

Question 46:
Range of the data is always from the data.
Solution:
False
It is not necessary as range is the difference of highest observation and lowest observation.

Question 47:
The data 12, 13, 14, 15, 16 has every observation as mode.
Solution:
True
Given data is 12, 13,14,15,16.
Here, each observation has same frequency, so every observation is a mode.

Question 48:
The range of the data 2, -5, 4, 3, 7, 6 would change, if 2 was subtracted from each value in the data.
Solution:
False
Range before subtraction by 2 = Highest observation – Lowest observation
= 7-(-5) = 7+ 5 = 12
Data after subtract by 2
= 2 -2,-5-2, 4-2, 3-2,7 -2, 6-2, i.e. 0,-7, 2, 1,5, 4
Range = Highest observation – Lowest observation = 5 – (-7) = 5+7 = 12
So, the range is same.

Question 49:
The range of the data 3, 7, 1, -2, 2, 6, -3, -5 would change, if 8 was added to each value in the data.
Solution:
False
Because, range before adding 8 = Maximum observation – Minimum observation
= 7-(-5) = 7+ 5 = 12
= 3 + 8,7 + 8,1 + 8, -2 + 8,2 + 8, 6+ 8, – 3 + 8, -5 + 8, i.e. 11,15, 9, 6, 10,14, 5, 3
So, the range is same. Range = Maximum observation – Minimum observation = 15-3 = 12

Question 50:
Calculate the mean, median and mode of the following data:
5, 10, 10, 12, 13
Are these three equal?
Solution:
Given data is 5,10,10,12,13.
Sum of all observations = 5+10+10+12 +13 = 50
Number of observations = 5

Question 51:
Find the mean of the first ten even natural numbers.
Solution:
First ten even natural numbers = 2, 4, 6, 8,10,12,14,16,18, 20.
Sum of all observations = 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20= 110

Question 52:
A data constitutes of heights (in cm) of 50 children. What do you understand by mode for the data?
Solution:
Since, mode is the observation that occurs most frequently in a set of observation.

Question 53:
A car seller collects the following data of cars sold in his shop:

(a) Which colour of the car is most liked?
(b) Which measure of central tendency was used in (a)?
Solution:
(a) Red colour of the car liked by people = 15
Black colour of the car liked by people = 20
White colour of the car liked by people = 17
Silver colour of the car liked by people = 12
Other colour of the car liked by people = 9
Hence, black colour of the car is the most liked.
(b) Mode concept used in (a).

Question 54:
The marks in a subject for 12 students are as follows:
31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29.
For the given data, find the
(a) Range
(b)Mean
(c) Median
(d) Mode
Solution:
Given data is 31,37, 35, 38, 42, 23,17,18, 35, 25, 35, 29.
Rearranging the given data in ascending order,
17,18, 23, 25, 29, 31,35, 35, 35, 37, 38, 42

Question 55:
The following are weights (in kg) of 12 persons:
70, 62, 54, 57, 62, 84, 75, 59, 62, 65, 78, 60
(a) Find the mean of the weights of the people.
(b) How many people weight above the mean weight?
(c) Find the range of the given data.
Solution:
(a) The weights of 12 persons are 70, 62, 54, 57, 62, 84, 75, 59, 62, 65, 78 and 60.
Sum of weights of 12 people
= 70+ 62 + 54+ 57 + 62+ 84+ 75+ 59 + 62 + 65 + 78 + 60 = 788
Number of observations (persons) = 12

(b) Weights above 65.66 are 70, 84, 75 and 78, i.e. 4 persons.
(c) Range = Maximum observation – Minimum observation = 84 – 54 = 30

Question 56:
Following cards are put facing down

What is the change of drawing out
(a) a vowel?
(b) a card marked LR
(c) A or I?
(d) a consonant?
Solution:
(a) We can clearly see that all the 5 letters are vowels, i.e. A, E, I, O, Hence, it is certain to draw a vowel, i.e. probability of drawing a vowel is 1.

Question 57:
For the given data below, calculate the mean of its median and mode
6, 2, 5, 4, 3, 4, 4, 2, 3
Solution:

Question 58:
Find the median of the given data, if the mean is
4.5. 5, 7, 7, 8, x, 5, 4, 3, 1, 2
Solution:

Question 59:
What is the probability of the sun setting tomorrow?
Solution:
Setting of the sun is a sure event. Hence, its probability is 1.

Question 60:
When a spinner with three colours given in figure is rotated, which colour has more chance to show up with arrow than the others?

Solution:
From the figure, area covered by the yellow colour is maximum out of the given three colours. Hence, chances of yellow colour to show up with arrow will be more.

Question 61:
What is the probability that a student chosen at random out of 3 girls and 4 boys is a boy?
Solution:
Given, total children = 7 = 4 boys and 3 girls.
So, favourable outcomes for a day = 4
Total number of possible outcomes = 7

Question 62:
The letters written on paper slips of the word MEDIAN and put in a bag. If one slip is drawn randomly, what is the probability that it bears the letter D?
Solution:
In the word ‘ MEDIAN’, there is only one D.
So, favourable  outcomes = number of letter D = 1
Total number of possible outcomes = 6

Question 63:
Classify, the following events as certain to happen, impossible to happen, may or may not happen.
(a) Getting a number less than 1 on throwing a die.
(b) Getting head when a coin is tossed.
(c) A team winning the match.
(d) Christmas will be on 25 December.
(e) Today moon will not revolve around the earth.
(f) A ball thrown up in the air will fall down after sometime.
Solution:
(a) Getting a number less than 1 on throwing a die is impossible, as a die does not have a number less than 1 on it.
(b) Getting head, when a coin is tossed may or may not happen as a coin has head and tail on its two faces. So, we might get a head or a tail on tossing it.
(c) A team may or may not win a match.
(d) Christmas is certain to happen on 25th
(e) It is impossible that moon will not revolve around the earth.
(f) It is certain to happen that a ball thrown up in the air will fall down after sometime due to gravity.

Question 64:
A die was thrown 15 times and the outcomes recorded were
5, 3, 4, 1, 2, 6, 4, 2, 2, 3, 1, 5, 6, 1, 2.
Find the mean, median and mode of the data.
Solution:
Given data is 5, 3, 4,1,2, 6, 4, 2, 2, 3,1,5, 6,1,2
Arranging the data in ascending order, we have
1, 1, 1,2, 2, 2, 2, 3, 3, 4, 4, 5,5, 6, 6.

Question 65:
Find the mean of first six multiples of 4.
Solution:

Question 66:
Find the median of first nine even natural numbers.
Solution:
First nine even natural numbers are
2,4,6,8,10,12,14,16,18.

Question 67:
The mean of three numbers is 10. The mean of other four numbers is 12. Find the mean of all the numbers.
Solution:

Question 68:
Find the mode of the given data.
10, 8, 4, 7, 8, 11, 15, 8, 4, 2, 3, 6, 8
Solution:
We know that, mode is the most frequent observation in the data.
∴ Mode = 8

Question 69:
Given below are heights of 15 boys of a class measured in centimetres:
128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.
Find
(a) the height of the tallest boy
(b) the height of the shortest boy
(c) the range of the given data
(d) the median height of the boys
Solution:
Given, height (data) of 15 boys of a class are
128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.
Arranging the given data in ascending order, we have
128, 129, 136, 138, 140, 140, 142, 142, 143, 144, 144, 146, 150, 152, 154
(a) By observing the data, height of the tallest boy = 154 cm
(b) By observing the data, height of the shortest boy = 128 cm
(c) Here, highest observation = 154 and lowest observation = 128
∴ Range = Highest observation – Lowest observation = 154-128 = 26cm

Question 70:
Observe the data and answer the questions that follow:
16, 15, 16, 16, 8, 15, 17
(b) Which data value can be put in the data so that the mode remains the same?
Atleast how many and which value(s) must be put into change the mode to 15?
(c) What is the least number of data values that must be put into change the mode to 17? Name them.
Solution:
Given data; 16,15,16,16,8,15,17
Arranging the given data in ascending order, we have 8, 15, 15, 16, 16, 16, 17
(a) As per the given data, 16 is the mode of data, since it has highest frequency, i.e. 3.
Now, if 15 is added to the given data, mode will get changed to 15 and 16, whereas if any other number, i.e. 8,16 or 17 is added, mode will remain same.
(b) Atleast two 15’s should be added to change the mode to 15. On adding two 15’s the frequency of 15 will be maximum, i.e. 4.
(c) We will have to add atleast three 17’s to change the mode to 17. On adding three 17’s, the frequency of 17 will be maximum, i.e. 4.

Question 71:
Age (in years) of 6 children of two groups are recorded as below:

(a) Find the mode and range for each group.
(b) Find the range and mode, if the two groups are combined together.
Solution:
From the given table, age of children in group A = 7 yr, 7 yr, 9 yr, 8 yr, 10 yr, 10 yr
Age of children in group 8 = 7 yr, 9 yr, 11 yr, 12 yr, 12 yr, 12 yr
(a) Mode in group A = 7 yr and 10 yr. [ 7 yr and 10 yr occurs most frequent, i.e.2times]
Range in group A = Maximum value – Minimum value = 10-7 = 3
Mode in groups = 12 yr                                                  [ 12yr is the most frequent, i.e. 3]
Range in group 8 = Maximum value – Minimum value = 12 – 7 = 5
(b) If both groups are combined together 7, 7, 7, 9, 9,11,8,12,10,12,10,12.
Mode = 7 and 12                                      [ 7 and 12 occurs most frequent, i.e. 3 times]
∴ Range = Maximum value – Minimum value = 12-7 = 5

Question 72:
Observe the given bar graph carefully and answer the questions that follow.

(a) What information does the bar graph depict?
(b) How many motor bikes were produced in the first three months?
(c) Calculate the increase in production in May over the production in January.
(d) In which month the production was minimum and what was it?
(e) Calculate the average (mean production of bikes in 6 months).
Solution:
(a) The given bar graph shows the production of motor bikes by XYZ automobiles Ltd. during January to June.
(b) Total number of motor bikes produced in first three months = Motor bikes produced in January + Motor bikes produced in February + Motor bikes produced in March
= 600 + 800 + 700
= 2100
(c) Increase in production in May over the production in January
= Production in May – Production in January = 900 – 600= 300
(d) By observing the graph, we can say that the production was minimum in the month of June, i.e. 500.

Question 73:
The bar graph given below shows the marks of students of a class in a particular subject:

Study the bar graph and answer the following questions:
(a) If 40 is the pass marks, then how many students have failed?
(b) How many students got marks from 50 to 69?
(c) How many students scored 90 marks and above?
(d) If students who scored marks above 80 are given merits, then how many merit holders are three?
(e)What is the strength of the class?
Solution:

Question 74:
Study the graph given below and answer the questions that follow:

(a) What information does the above bar graph represent?
(b) In which year was production the least?
(c) After which year was the maximum rise in the production?
(d) Find the average production of rice during the 5 years.
(e) Find difference of rice production between years 2006 and 2008.
Solution:
After studying the bar graph, we have
Production of rice in 2005 = 50 million tonne
Production of rice in 2006 = 40 million tonne
Production of rice in 2007 = 70 million tonne
Production of rice in 2008 = 50 million tonne
Production of rice in 2009 = 60 million tonne
(a) The bar graph shows the production of rice in million tonne by a country during years 2005 to 2009.
(b) The production of rice was the least in 2006, i.e. 40 million tonne.
(c) The maximum production of rice was in 2007. The production rose after 2006.

(e) Production in 2006 = 40 million tonne and production in 2008 = 50 million tonne
Difference = 50 – 40 = 10 million tonne.

Question 75:
Study the bar graph given below and answer the questions that follow:

(a) What information is depicted from the bar graph?
(b) In which subject is the student very good?
(c) Calculate the average marks of the student.
(d) If 75 and above marks denote a distinction, then name the subjects in which the student got distinction.
(e) Calculate the percentage of marks the student got out of 500.
Solution:
(a) he given bar graph shows marks obtained by a student in different subjects out of 100.
(b) Subject in which student is very good, Maths as he scored highest marks, i.e. 82

Question 76:
The bar graph given below represents the circulation of newspapers (dailies) in a town in six languages (the figures are approximated to hundreds).

Study the bar graph and answer the following questions:
(a) Find the total number of newspapers read in Hindi, Punjabi, Urdu, Marathi and Tamil.
(b) Find the excess number of newspapers read in Hindi than those in English.
(c) Name the language in which the least number of newspapers are read.
(d) Write the total circulation of newspaper in the town.
Solution:
Number of newspapers in Urdu = 200
Number of newspapers in Tamil = 100
Number of newspapers in English = 500
Number of newspapers in Hindi = 800
Number of newspapers in Marathi = 300
Number of newspapers in Punjabi = 400

Question 77:
Study the double bar graphs given below and answer the following questions:

(a) Which sport is liked the most by class VIII students?
(b) How many students of class VII like Hockey and Tennis in all?
(c) How many students are there in class VII?
(d) For which sport is the number of students of class VII less than that of class VIII?
(e) For how many sports students of class VIII are less than class VII?
(f) Find the ratio of students who like Badminton in class VII to students who like Tennis in class VIII.
Solution:
(a) By observing the graph, we can say that the height of the bar corresponding to cricket for class VIII student is largest. Hence, cricket is liked the most by class VIII students.
(b) Height of bar corresponding to hockey and tennis for class VII are 7 and 10 respectively. So, total students of class VII who like hockey and tennis = 7 + 10 =17
(c) Total number of students in class VII = Sum of heights of all the bars for class VII
= 7 + 16+18+10+14=65
(d) The sport for which number of students of class VII is less than that of class VIII will be that for which height of bar is less.
By observing the graph in case of cricket height of bar is less for class VII as compared to class VIII.
(e) We can clearly see from the double bar graph for Hockey, Football, Tennis and Badminton, the number of students are less for class VIII as compared to class VII.
(f) Number of students who like badminton in class VII = 14 and number of students who like tennis in class VIII = 7
∴ Required ratio = 14:7 = 2:1

Question 78:
Study the double bar graph shown below and answer the questions that follow:

(a) What information is represented by the above double bar graph?
(b) In which month sales of brand A decreased as compared to the previous month?
(c) What is the difference in sales of both the brands for the month of June?
(d) Find the average sales of brand B for the six months.
(e)List all months for which the sales of brand B was less than that of brand
(f) Find the ratio of sales of brand A as compared to brand B for the month of January.
Solution:
(a) The above double bar graph compares the sale of brands A and 6 during the months of January to June.
(b) We can clearly see from the double bar graph that sales for brand A reduced in the month of March compared to that of February.
(c) Sales of brand A in June = 157 lakh and sales of brand 6 in June = Rs. 54 lakh
Difference in sales = 57 – 54 = Rs. 3 lakh

(e) We can clearly see from the double bar graph that sales of brand S is less than sales of brand A in the month of April and June.
(f) Sales of brand A in January = 31 and sales of brand S in January = 36
∴Required ratio = 31/36 or  31: 366

Question 79:
Study the double bar graph shown given below and answer the question that follow:

(a) What information is compared in the above given double bar graph?
(b)Calculate the ratio of minimum temperatures in the year 2008 to the year 2009 for the month of November.
(c) For how many months was the minimum temperature in the year 2008 greater than that of year 2009? Name those months.
(d) Find the average minimum temperature for the year 2008 for the four months.
(e) In which month is the variation in the two temperatures maximum?
Solution:
(a) The above double bar graph compares the minimum temperature during the month November to February for the years 2008 and 2009.
(b) Minimum temperature of November in year 2008 = 18°C
Minimum temperature of November in year 2009 = 15°C
∴ Required ratio = 18/ 15 = 18:15 = 6:5
(c) We can clearly see from the double bar graph that the minimum temperature in the year 2008 greater than that of the year 2009 for the month of February and November.

From the above table, it is clear that for the month of February variation in two temperatures is maximum.

Question 80:
The following table shows the average intake of nutrients in calories by rural and urban groups in a particular year. Using a suitable scale for the given data, draw a double bar graph to compare the data.

Solution:
Steps to construct the bar graphs are as follows:
Step I Firstly, we draw two lines perpendicular to each other on a graph paper and call them horizontal and vertical axes.
Step II Along the horizontal axis, we mark the foodstuff and along the vertical axis, we mark the intake of nutrients (calories).
Step III We choose a suitable scale to determine the heights of bars. Here, we choose the scale as 1 small division to represent
20.
Step IV First, we draw the bars for rural and then bars of urban for different foodstuff.
Bars for rural and urban are shaded separately and the shading is shown at the top right corner of the graph paper.

Question 81:
Study the double bar graph and answer the questions that follow:

(a) What information does the double bar graph represent?
(b)Find the total number of boys in all sections of class VII.
(c) In which sections, number of girls is greater than number of boys?
(d) In which section, the number of boys is the maximum?
(e) In which section, the number of girls is the least?
Solution:
(a) The above graphs shows the number of students (boys and girls) in different sections of class VII.
(b) It is clear from the graph, total number of boys in all sections of class VII = Sum of heights of all the bars corresponding to boys in different sections = 15+ 30 + 20 + 20 + 25=110
(c) It is clear from the graph that in sections VII A and VII D, the number of girls are greater than the number of boys.
(d)From the graph, it is clear that in section VII B, number of boys is maximum.
(e) From the graph, it is clear that in section VII C, number of girls is minimum,

Question 82:
In a public library, the following observations were recorded by the librarian in a particular week.

(a) Draw a double bar graph choosing a appropriate scale.
(b) On which day, the number of readers in the library was maximum?
(c) What is the mean number of magazine readers?
Solution :
Steps to construct the bar graphs are as follows:
Step I We draw two lines perpendicular to each other on a graph paper and call them horizontal and vertical axes.
Step II Along the horizontal axis, we mark the days and along the vertical axis, we mark the readers.
Step III We choose a suitable scale to determine the heights of bars.Here, we choose the scale as 1 small division to  represent 50.
Step IV First, we draw the bars for newspaper readers and then bars for magazine readers for different days.

Bars for newspapers and magazine readers are shaded separately and the shading is shown in the top right corner of the graph paper.

Question 83:
Observe the following data:

(a) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
(b) Which class has the maximum number of students?
(c) In which class, the difference of total students and number of students present is minimum?
(d) Find the ratio of number of students present to the total number of students of class IX.
(e) What percentage of class VI students were absent?
Solution:

Question 84:
Observe the following data:

(a) Draw a bar graph to represent the above given information.
(b) On which day of the week was the sales maximum?
(C) Find the total sales during the week.
(d) Find the ratio of the minimum sale to the maximum sale.
(e) Calculate the average sale during the week.
(f) On how many days of the week was the sale above the average sales?
Solution:
(a) In order to construct a bar graph representing the above data, we follow the following steps:
Step I Take a graph paper and draw two mutually perpendicular lines OX and OY. Call OX as the horizontal axis and OY as the vertical axis.
Step II Along OX, mark days and along OY, mark number of mobile phone sets sold.
Step III Along OX, choose the uniform (equal) width of the bars and the uniform gap between them, according to the space available for the graph,
Step IV Choose a suitable scale to determine the heights of the bars, according to the availability of space. Here, we choose 1 small division to represent 5 mobile sets.

Question 85:
Below is a list of 10 tallest buildings in India.
This list ranks buildings in India that stand atleast 150 m (492 ft.) tall, based and standard height measurement. This includes spires and architectural details but does not include antenna marks. Following data in given as per the available information till 2009. Since, new buildings are always under construction, go online to check new taller buildings.
Use the information given in the table about skyscrapers to answer the following questions:

(b) The average height of one storey for the buildings given in (a) is _____.
(c) Which city in this list has the largest percentage of skyscrapers?
(d) What is the range of data?
(e) Find the median of the data.
(f)Draw a bar graph for given data.
Solution:

Question 86:
The marks out of 100 obtained by Kunal and Soni in the half yearly examination are given below:

(a) Draw a double bar graph by choosing appropriate scale.
(b) Calculate the total percentage of marks obtained by Soni.
(c) Calculate the total percentage of marks obtained by Kunal.
(d) Compare the percentages of marks obtained by Kunal and Soni.
(e) In how many subjects did Soni get more marks than Kunal? Which are those subjects?
(f) Who got more marks in S. Science and what was the difference of marks?
(g) In which subject the difference of marks was maximum and by how much?
Solution:
(a) Steps to construct the bar graphs are as follows :
Step I We draw two lines perpendicular to each other on a graph paper and call them horizontal and vertical axes.
Step II Along the horizontal axis, OX mark the subjects and along vertical axis, OY mark the marks obtained.
Step III We choose a suitable scale to determine the heights of bars. Here, we choose the scale as 1 small division to represent 5 marks.
Step IV First, we draw the bars for Kunal and then bars for Soni for different years.
Bars for Kunal and Soni shaded separately and the shading is shown in the top right corner of the graph paper.

Question 87:
The students of class VII have to choose one club from Music, Dance, Yoga, Dramatics, Fine arts and Electronics clubs. The data given below shows the choices made by girls and boys of the class. Study the table and answer the questions that follow:

(a) Draw a double bar graph using appropriate scale to depict the above data.
(b) How many students are there in class VII?
(c) Which is the most preferred club by boys?
(d) Which is the least preferred club by girls?
(e)For which dub the difference between boys and girls is the least
(f) For which dub is the difference between boys and girls the maximum?
Solution:
(a) Steps to construct the bar graph are as follows :
Step I We draw two lines perpendicular to each other on a graph paper and call them horizontal and vertical axes.
Step II Along the horizontal axis, OX mark the clubs and along the vertical axis, OY mark the number of boys and girls.
Step III We choose a suitable scale to determine the heights of bars.
Here, we choose the scale as 1 small division to represent 2.
Step IV First, we draw the bars for girls and then bars for boys for different years. Bars for girls and boys are shaded separately and the shading is shown in the top right corner of the graph paper

(b) Total students in class VII
= 15+ 12 + 24 + 16+ 10+ 8+ 19 + 17 + 27 + 11 + 21+ 30 =210
(c) From the given data, we can say that most preferred club by boys is Electronics.
(d) From the given data, we can say that least preferred club by girls is Yoga.
(e) It is clear from the given data in Yoga and Dramatics, the difference between boys and girls is the least, i.e. (19 -17) = 2
(f) It is clear from the given data in Fine Arts the difference between boys and girls is maximum, i.e. (27 -11) = 16

Question 88:
The data given below shows the production of motor bikes in a factory for some months of two consecutive years.

Study the table given above and answer the following questions:
(a) Draw a double bar graph using appropriate scale to depict the above information and compare them.
(b) In which year was the total output the maximum?
(c) Find the mean production for the year 2007.
(d) For which month was the difference between the production for the two years the maximum?
(e) In which month for the year 2008, the production was the maximum?
(f) In which month for the year 2007, the production was the least?
Solution:
(a) Steps to construct the bar graphs are as follows:
Step I We draw two lines perpendicular to each other on a graph paper and call them horizontal and vertical axes.
Step II Along the horizontal axis, OX mark the months and along the vertical axis, OY mark the production of motor bikes.
Step III We choose a suitable scale to determine the heights of bars.
Here, we choose the scale as 1 big division to represent 400.
Step IV First, we draw the bars for Year 2008 and then bars for Year 2007 for different months.

Bars for year 2008 and year 2007 months are shaded separately and the shading is shown in the top right corner of the graph paper.

(d) It is clear from the given data in May the difference between the production for the two years in maximum, i.e. 1300.
(e) In August the production was maximum, i.e. 6000 as compared to other months of year 2008.
(f) In February the production was minimum, i.e. 2800 as compared to other months of year 2007.

Question 89:
The table below compares the population (in hundreds) of 4 towns over two years:

Study the table and answer the following questions:
(a) Draw a double bar graph using appropriate scale to depict the above information.
(b) In which town was the population growth maximum?
(c) In which town was the population growth least?
Solution:
(a) Steps to construct the bar graph are as follows :
Step I We draw two lines perpendicular to each other on a graph paper and call them horizontal and vertical axes.
Step II Along the horizontal axis, OX mark the towns and along the vertical axis, OY mark the population.
Step III We choose a suitable scale to determine the heights of bars. Here, we choose the scale as 1 small division to represent
500,
Step IV First, we draw the bars for year 2007 and then bars for year 2009 for different towns.

Bars for year 2007 and 2009 are shaded separately and the shading is shown in the top right corner of the graph paper.
vc
(b) It is clear from the graph, the population growth of town D was maximum.
(c) It is clear from the graph, the population growth of town A was minimum.

Question 90:
The table below gives the data of tourists visiting 5 hill stations over two consecutive years. Study the table and answer questions that follow:

(a) Draw a double bar graph to depict the above information using appropriate scale.
(b) Which hill station was visited by the maximum number of tourists in 2008?
(c) Which hill station was visited by least number of tourists in 2009?
(d) In which hill stations was there increase in number of tourists in 2009?
Solution:
(a) Steps to construct the bar graph as follows:
Step I We draw two lines perpendicular to each other on a graph paper and call them horizontal and vertical axes.
Step II Along the horizontal axis, OX mark the hill stations and along the vertical axis, OY mark the tourist visitors.
Step III We choose a suitable scale to determine the heights of bars. Here, we choose the scale as 1 small division to represent 400 tourists.
Step IV First, we draw the bars for year 2008 and then bars for year 2009 for different hill stations.
Bars for years 2008 and 2009 are shaded separately and the shading is shown in the top right corner of the graph paper,

(b) It is clear from the given data that in year 2008 tourists visit Mussoorie the most maximum.
(c)It is clear from the given data that in year 2009 tourists visit Manali the least.
(d) From the graph, we can say that in 2009, there is increase in tourist visitors in the places; Manali, Nainital, Mussoorie and Kullu.

Question 91:
The table below gives the flavours of ice-cream liked by children (boys and girls) of a society.

Study the table and answer the following questions:
(a) Draw a double bar graph using appropriate scale to represent the above information.
(b) Which flavour is liked the most by the boys?
(c) How many girls are there in all?
(d) How many children liked chocolate flavour of ice-cream?
(e) Find the ratio of children who liked strawberry flavour to vanilla flavour of ice-cream.
Solution:

(b) On observing the bar graph, we can say that boys like butterscotch the most because the bar for butterscotch in case of boys is of highest length, i.e. 13.
(c) Total number of girls = Sum of heights of bars corresponding to girls
= 8+12 + 7 + 9+10=46
(d)Number of children who like chocolate flavour = Sum of heights of bars for both boys and girls corresponding to chocolate
= 9 + 12 = 21
(e) Total number of children who like strawberry =3+7=10
Total number of children who like vanilla =4+8=12
∴ Ratio of children who like strawberry flavour to vanilla flavour of ice-cream
= 10:12 = 5:6

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# Basic Statistical Measures

#### chrisyuen

1. Homework Statement

The pass mark of an examination is set at 40. The following table shows some summary statistics of the marks (x) of the 200 students who took the examination.

Mark Range: x >= 40, x < 40
Number of students: 160, 40
Mean: 64.0, 32.0
Standard deviation: 6.0, 4.0

The teacher wants to scale the marks so that more students will pass the examination. The new mark corresponding to x is

y = 50 + $$\frac{5}{6}$$(x - 40), if x >= 40
y = $$\frac{5x}{4}$$ if x < 40

(a) Find the mean and standard deviation of the new marks of the 200 students.
(b) The median of the original 200 marks is 52. Find the median of the new marks.

(a) 64; 13
(b) 60)

2. Homework Equations

Basic Formulae for Statistical Measures

3. The Attempt at a Solution

I don't know how to find the standard deviation for part (a) and the median for part (b).

Can anyone tell me how to solve them?

Thank you very much!

Last edited:
Related Calculus and Beyond Homework Help News on Phys.org

#### chrisyuen

I know that part (b) can be solved using linear transformation y = ax + b.

50 + $$\frac{5}{6}$$(52 - 40) = 60 but not $$\frac{5(52)}{4}$$.

Can anyone tell me the reason?

Thank you very much!

Last edited:

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# Hydration health literacy in the elderly

### BACKGROUND:

Inadequate hydration in the elderly is associated with increased morbidity and mortality. However, few studies have addressed the knowledge of elderly individuals regarding hydration in health and disease. Gaps in health literacy have been identified as a critical component in health maintenance, and promoting health literacy should improve outcomes related to hydration associated illnesses in the elderly.

### METHODS:

We administered an anonymous survey to community-dwelling elderly (n = 170) to gauge their hydration knowledge.

### RESULTS:

About 56% of respondents reported consuming >6 glasses of fluid/day, whereas 9% reported drinking ≤3 glasses. About 60% of respondents overestimated the amount of fluid loss at which moderately severe dehydration symptoms occur, and 60% did not know fever can cause dehydration. Roughly 1/3 were not aware that fluid overload occurs in heart failure (35%) or kidney failure (32%). A majority of respondents were not aware that improper hydration or changes in hydration status can result in confusion, seizures, or death.

### CONCLUSIONS:

Overall, our study demonstrated that there were significant deficiencies in hydration health literacy among elderly. Appropriate education and attention to hydration may improve quality of life, reduce hospitalizations and the economic burden related to hydration-associated morbidity and mortality.

## 1Introduction

A number of common hydration-related medical conditions in the geriatric population are associated with either excess total body fluid (overhydration), or reduced total body fluid (dehydration) [1–10]. Dehydration occurs when there is excess fluid loss from the body, either due to an illness, exposure to high temperatures, exertion with inadequate fluid intake or use of diuretic medications. This can result in serious imbalance of sodium ranging from hypo to hypernatremia which if not treated promptly, could result in significant morbidity and mortality [1, 4–6]. The symptoms of dehydration can range from simple dizziness and confusion to seizures and death. Some of the physical signs of dehydration that have demonstrated good specificity for detection include dry axillae, sunken eyes, and a delayed capillary refill time [2, 3].

In some individuals, the loss of as little as 2-3% of body fluid can cause physical and cognitive impairment [4]. The elderly population is at an increased risk for dehydration for a number of reasons, including a decrease in the thirst sensation, a decrease in renal perfusion, an altered sensitivity to antidiuretic hormone and neurocognitive deficits [1, 4–7] Notably, Rowat et al. identified 4 independent risk factors for dehydration upon admission to a hospital: 1) older age, 2) female gender, 3) total anterior circulation syndrome, and 4) prescribed diuretics [8].

Clinically, dehydration is a major predictor of morbidity and mortality in admitted patients [8, 9]. Rowat et al. assessed dehydration in hospitalized stroke patients and discovered that dehydrated patients were significantly more likely than hydrated patients to become dependent upon others at discharge or die during hospitalization [8]. Dehydration following a stroke also increases the risk of venous thromboembolism, and this is associated with poor health outcomes [8].

In addition to thromboembolism, there are numerous other consequences of dehydration among the elderly population, including delirium, confusion, infections, falls, and fractures [10–12]. Lastly, Hodgkinson et al. found that semi-independent patients in nursing homes who appear to be capable of obtaining their own fluids, but who cannot do so in practice, are most at risk for dehydration [13]. It is estimated that cognitively impaired residents in nursing facilities are at the highest risk of dehydration and more than one-third suffer from dehydration [14, 15]. In these cases, healthcare professionals do not present these patients with fluids because they do not perceive this group as being at risk for dehydration [15].

Dehydration also presents a tremendous economic burden some of which is potentially preventable [16]. A large retrospective study using the Healthcare Cost and Utilization Project (HCUP) project data revealed that the average age for patients admitted with the principal diagnosis of dehydration was 80.4 years. Approximately 64% of these were community dwelling white women [17]. The average length of stay (LOS) for dehydration in the HCUP data was 4.6 days and the total hospitalization charge per person was $7,442 [17]. The elderly population is also at risk for overhydration. Overhydration, or fluid overload, is caused by a number of conditions, including heart failure [18, 19], kidney failure [20, 21], and protein deficiency [22]. Iatrogenic overhydration can also occur as a result of receiving intravenous fluids [23], blood transfusions [24], and steroids [25]. The consequences of overhydration range from mild to life-threatening and include congestive heart failure and pulmonary edema, [26–28], confusion [29, 30], high blood pressure, seizure, and even death [31, 32]. The electrolyte abnormalities in elderly surgical patients and critically ill are often due to overhydration secondary to excess or inappropriate infusion of intravenous fluids [32–34]. Hence, overhydration is an independent risk factor for morbidity and mortality in elderly people with heart failure, acute or chronic renal failure or for those on dialysis [4, 5, 33, 34]. Despite numerous studies that describe why the elderly population is at an increased risk for hydration-related health issues compared to the younger population, there is little information on how much fluid elderly people consume or the health literacy of this population about proper hydration [13]. One of the few studies that investigated this, Goodman et al., concluded from the National Cancer Institute’s 2007 Food Attitudes and Behaviors Survey that a significantly greater number of individuals 55 years of age or older drink fewer than 4 cups of water per day compared to individuals between 18 and 34 years old (47% vs. 43%, p = 0.04) [35, 36]. This finding supported those of Sebastian et al. who found that while those 20–39 years of age reported drinking 4.7–5 cups of water/day, those 60+ years old reported drinking only 3.1–3.5 cups/day [37, 38]. While these data indicate that the elderly population consumes less water than the younger population, more work needs to be done to determine the specific amount of fluid that the elderly consume and to understand the elderly population’s general knowledge of hydration. In addition, there has been minimal research into how well elderly individuals understand the signs and symptoms of dehydration and overhydration. Since the elderly are highly susceptible to problems associated with hydration, we conducted a survey to understand how much fluid elderly individuals consume on a daily basis and to determine their knowledge about optimal hydration status, the signs and symptoms of dehydration and overhydration, and some of the common associated medical conditions. ## 2Materials and methods ### 2.1Design This was a cross-sectional study based using an anonymous survey and a convenience sample methodology. The questionnaire was designed to evaluate the health literacy of older adults in the geriatric age-group regarding the importance of hydration in health and different common disease conditions encountered in the elderly. The survey comprised of 5 demographic questions and 10 structured hydration related questions which addressed types and quantity of fluids consumed, the importance of hydration for health and the problems associated with dehydration or overhydration (Fig. 1). The study was approved by the Institutional Review Board at the University of Arkansas for Medical Sciences (UAMS) (IRB protocol #202655). ##### Fig.1 Hydration questionnaire utilized in the study. Demographic questions have not been included in this figure. ### 2.2Subjects The survey was completed by 170 elderly, community-dwelling individuals (over the age of 60) who were patients at the Thomas and Lyon Longevity Clinic at the UAMS Reynolds Institute on Aging. A trained research technician administered the survey to participants. The participants either completed the survey themselves or the research technician read the questions and possible answers to them, and the participant indicated the answers verbally. ### 2.3Analysis The survey results were analyzed with SAS software (version 9.3, SAS Institute Inc.). Categorical variables are presented as counts and percentages that were calculated with the PROC FREQ SAS procedure. Responses to questions were compared by group with either the chi-square test or Fisher’s exact test for contingency tables with cells having expected frequencies of 5 or less. The chi-square and Fisher’s exact tests were performed with the PROC FREQ SAS procedure with the options “chisq” and “fisher.” The α cut-off for significance was accepted as p < 0.05. ## 3Results ### 3.1Study participants The demographic characteristics of the participants are detailed in Table 1. All of the survey respondents were community-dwelling, and most lived in the Central Arkansas area. The majority of survey respondents (57%) were between 70 and 79 years old, 80% were White, Non-Hispanic, and 20% were African Americans. There were 52% females. The majority were college graduates or greater (57%), but 35% had less than a high school education. ##### Table 1 Demographics (n = 170)  Percent Age 60–69 20.4 70–79 57.4 80–89 20.4 90–99 1.9 Race White, non-Hispanic 80.0 African American 20.0 Gender Female 51.9 Male 48.1 Education Less than high school 35.0 Some college 8.4 College graduate or more 56.6 ### 3.2Fluid intake Our survey began by gauging how much and what type of fluid the participants consumed each day through recall of fluid intake on an average day. We found that the majority of respondents (56%) drank more than 6 glasses of fluid each day, with 15% drinking 9 or more glasses (Fig. 2A). Over 35% reported drinking at least 4 to 6 glasses each day, and only 9% drank 3 glasses or fewer (Fig. 2A). ##### Fig.2 Self-reported A) amounts and B) types of fluids the survey respondents consumed per day. Most respondents consumed 4–9 glasses of fluid per day, and the most popular drinks were water and coffee. “Other” drinks included milk, fruit and vegetable juices, and alcoholic beverages (e.g. beer or wine). When asked about the kinds of fluids they drank, 90% reported drinking water, 66% drank coffee, and 47% drank tea (Fig. 2B). Only 22% reported drinking soda (e.g., Coke or Pepsi) (Fig. 2B). With respect to other kinds of fluids, about 12% of respondents mentioned drinking milk, fruit or vegetable juice and alcoholic beverages (e.g., beer or wine). ### 3.3Importance of hydration We next determined how much each participant knew about the importance of fluid intake for the function of the body. The majority of respondents (79%) were aware that adequate fluid intake was important for eliminating waste from the body, and at least 60% of respondents had significant knowledge about hydration to identify that cooling of the body, metabolism, and maintaining good circulation were related to adequate fluid intake (p < 0.05, Fig. 3A). While the majority of respondents appeared to understand the physiologic functions of fluid intake, only 34% correctly identified the amount of fluid loss (3-4% of body fluid) required for the signs and symptoms of dehydration to develop (Fig. 3B). The majority of respondents (60%) reported that the signs and symptoms of dehydration begin after the loss of 10% or higher of body fluid. This represented a significant knowledge deficit in the elderly regarding how critically important fluids are for the body (p < 0.05, Fig. 3B). ##### Fig.3 Survey respondents were asked about A) The importance of adequate fluid intake for bodily function. About 60–80% displayed sufficient hydration literacy regarding specific body functions requiring adequate fluid intake. B) Only 34% of respondents were able to correctly answer at what percentage of fluid loss dehydration signs and symptoms would begin to appear. *P-value <0.05. ### 3.4Conditions that cause dehydration or overhydration The participants were also surveyed about their knowledge of medical conditions that can cause dehydration or overhydration. A significant percentage of respondents were aware that diarrhea (68%) orvomiting (59%) caused dehydration (p < 0.05, Fig. 4A). However, a significant gap in hydration health literacy was observed in 60% of the respondents when they failed to associate fevers or kidney failure with fluid loss (p < 0.05, Fig. 4A). Only about 55% of the respondents were aware that diuretics and excessive perspiration can cause dehydration (Fig. 4A). ##### Fig.4 The survey included questions asking about A) Conditions that cause excess fluid loss and B) Conditions that cause excess fluid retention. Only ∼60% percent of respondents were able to correctly identify conditions associated with excess fluid loss (diarrhea and vomiting) and excess fluid retention (heart failure and kidney failure). *P-value<0.05. Health literacy regarding overhydration was also limited but a significant percentage of respondents seemed to be aware that heart failure (65%) and kidney failure (68%) were conditions where excess fluid accumulated in the body (p < 0.05, Fig. 4B). However, there were serious knowledge gaps regardingcertain conditions and fewer than one-third of respondents knew that liver failure (30%), receiving excess intravenous fluids or a blood transfusion (29%), receiving steroids (28%) or protein deficiency (23%), could result in problems with overhydration (p < 0.05, Fig. 4B). ### 3.5Effects of dehydration and overhydration We were also interested in learning how much the respondents knew about the effect of dehydration and overhydration on the concentration of sodium in the blood. Approximately two-thirds of respondents answered that reduced fluid intake could increase sodium and excess fluid intake could reduce sodium. However, just over 60% of the respondents believed that an increased fluid intake would reduce potassium concentrations, and nearly 20% believed that reduced fluid intake, or dehydration, would actually reduce the sodium levels in the blood (p < 0.05, Fig. 5). ##### Fig.5 Survey respondents were asked about how reduced or increased fluid intake would affect sodium levels in the blood. A small majority of the subjects believed that there was increase in sodium level with reduced fluid intake, while a minority of the subjects believed that sodium level increased with increased fluid intake. Yes vs No; *P-value<0.05. ### 3.6Symptoms of dehydration and overhydration Lastly, there were significant deficits in the health literacy of respondents about medical complications associated with dehydration and overhydration. The most common association with that the respondents made with dehydration was the symptom of dizziness (70%, p < 0.05, Fig. 6A). However, a high percentage of respondents were not aware that low blood pressure (54%), fainting (54%), increased heart rate (58%), excessive sleepiness (70%), seizures (78%) and even death (72%) could be a consequence of dehydration (p < 0.05, Fig. 6A). ##### Fig.6 Signs and symptoms of A) reduced body fluid and B) excess body fluid were addressed by the survey. A significant number of respondents were hydration literate for one symptom each in regards to reduced and excess body fluid. For the other signs and symptoms, there was a knowledge deficit, for which certain symptoms was significant. *P-value<0.05. With respect to overhydration, the majority of participants knew that swelling of the ankles (84%) was a sign of overhydration (p < 0.05, Fig. 6B). However, there was a significant knowledge deficit knew regarding seizures (80%), confusion (65%), and death (71%) as complication of overhydration (p < 0.05, Fig. 6B). Common consequences of fluid overload in the elderly such as shortness of breath and high blood pressure were also only recognized by about 50% of the respondents. ## 4Discussion Here, we report the results of a survey conducted to help identify health literacy needs of the elderly regarding the importance of hydration, especially with respect to various health conditions. Our results uncover significant gaps in hydration health literacy in the elderly in spite of the fact that the majority of our survey respondents reported that they consumed an adequate amount of fluid on a daily basis and acknowledged that proper hydration was important for eliminating waste. However, knowledge regarding temperature control, metabolism and circulation was less optimal and was reflected in answers to questions addressing signs and symptoms in addition to medical complications associated with inadequate hydration. Interestingly, our findings on the amount of fluid consumed mirror the results of a study by Lindeman et al. which reported that 71% of community-dwelling elderly adults (mean age 74.1 years old) drank at least 6 glasses of water per day [39]. Other studies reported the likelihood of drinking fewer than 4 cups of water per day to be significantly higher among people over 55 years of age as opposed to young adults (47% vs. 43%, p = 0.04) [35, 36]. Specifically, the 2005-2008 NHANES study reported that adults over age 60 consumed just over 3 cups of water per day (3.1–3.5 cups/day), more than a cup less than those 20–39 years of age (4.7–5.0 cups/day) [37, 38]. However, these discrepancies could have been the result of recall bias, especially in patients with dementia, unless they or their caregivers had been instructed to document fluid intake [14]. How much fluid should elderly people actually drink each day? The standard recommendation is to drink 8 glasses of fluid per day [40], but there is some disagreement. Both Lindeman et al. and Negoianu et al. suggest that elderly people who drink 8 glasses of water per day may actually be overhydrated [39, 41]. Caution does need to be exercised in the elderly because many older people have reduced renal and/or cardiac function and a one-size-fit-all approach of 8 glasses might cause fluid-overload and exacerbate heart failure. In fact, heart failure patients are often fluid restricted to 1–1.5 liters of fluid per day in addition to being on diuretics [42, 43]. European Food and Safety Agency (EFSA) has set guidelines for adequate intake of water for healthy men and women at 2.5 L/d and 2.1 L/day respectively [44]. A recent study of total fluid intake of adults collected 7–day fluid records from adults in 13 different countries and showed wide geographical variation in the total amount of fluid consumed with only 40% of men and 60% of women complying with the EFSA guidelines [44]. This study, although large, was limited by the percentage of people in the geriatric age-group and did not have any objective measurement of hydration status. It is important to remember that overhydration occurs not only in common conditions of heart and renal failure, it is also iatrogenic in the hospital setting and is independently associated with all cause morbidity and mortality, especially with more than 7% of positive fluid balance [45, 46]. Hence, it will be useful to have accurate and portable tools for measurement of hydration status, especially for the medically complex geriatric population with renal insufficiency and/or cardiac decompensation. A number of instruments have been developed to measure hydration status but the sensitivity and specificity of bioelectric impedance devices still requiresrefinement [47]. Why is there so much emphasis on fluid intake? Dehydration has been identified as an independent “ambulatory care-sensitive condition” or ACSC by the Agency for Healthcare Research and Quality (AHRQ) in the United Sates [17, 48]. In a large healthcare utilization study of more than 79,000 elderly patients admitted with a principal diagnosis of dehydration, about 50% had urinary tract infections and approximately the same percentage were listed as having respiratory and/or cardiac conditions [17]. A report from 2015 concluded that$1.36 billion was spent to treat elderly patients hospitalized for dehydration [16]. Hence, one might conclude that with appropriate training and education, early recognition and management of urinary tract infections, pneumonias, and heart failure might result in substantially reduced costs for dehydration-related admissions to thehospital.

There are a number of reasons why older individuals have reduced fluid consumption. The age-associated reduction of the thirst mechanism is complex and is driven partially by changes in the hypothalamic thirst sensors as well as the peripheral baroreceptors, both of which degenerate with age to a variable extent in individuals [48–50]. Stachenfeld suggested that the mechanism for diminished thirst in the elderly was secondary to a significantly reduced ability to sense a volume deficit although their ability to respond to increased osmolality was similar to that of younger adults [50]. This hypothesis is supportive of the greater age-associated atrophy of the carotid baroreceptors, which is also a cause for orthostatic hypotension in the geriatric population, especially with dehydration [50–52]. Apart from diminished thirst, older individuals often consume less fluids because of problems associated withurinary incontinence, ambulation, manual dexterity or cognition, which predisposes them to dehydration often in poorly staffed nursing facilities [52–54].

We also explored questions related to sodium and potassium balance relative to hydration because in the out-patient setting laboratory results are discussed with the patients and/or caregivers and instructions are frequently provided regarding fluids, salt or potassium intake. Reduced water intake or free water loss is generally associated with hypernatremia, or in mild cases with normal sodium concentration [7, 43]. However, in hypovolemic dehydration due to any reason (diarrhea, vomiting, burns, diuretics), there can be significant hyponatremia [43]. Overhydration can also result in hyponatremia of varying degrees and is frequently iatrogenic in elderly hospitalized patients [7, 43]. Interestingly, the majority of our participants believed that reduced fluid intake would have no effect on sodium balance. This response was concerning because it demonstrated that the elderly participants were not aware of the effect fluid intake can have on sodium balance, and the critical importance of sodium and water regulation in health and disease.

A key pituitary hormone involved in the regulation of hydration is vasopressin or anti-diuretic hormone (ADH), which is normally released in response to dehydration to signal water conservation by the nephrons [54]. Abnormal release of vasopressin occurs in the body by malignant tumors, in response to cancer medications, opiates, pulmonary infections, brain inflammation/ischemia or for idiopathic reasons, in what is termed the syndrome of inappropriate antidiuretic hormone secretion (SIADH) [54]. Management of hyponatremia is complex and can range from simple water restriction and loop diuretics to hypertonic saline or newer drugs such as the vasopressin receptor antagonists [55]. There are a few recent studies that suggest that high levels of vasopression in the blood might be associated with insulin resistance, increased hepatic steatosis and with an increased risk for development of type 2 diabetes mellitus [56–58]. Although more conclusive evidence is required, it will certainly be a very cost effective strategy to prudently encourage water consumption in order to reduce insulin resistance. A study by Godfrey et al. recommends that caregivers take a personalized approach to hydration care, making the act of drinking fluids a pleasurable experience by increasing the aesthetic appearance of a beverage or promoting social interactions [59]. This could be a promising tactic to help older people drink more fluid, and this subject will certainly benefit from furtherstudy.

### 4.1Gaps in health literacy

Our data indicate that older adults are not fully aware of medical conditions that cause dehydration or overhydration. For example, only about one-third of respondents knew that the loss of 3 to 4% of body fluid can lead to dehydration, and few realized that even a simple fever in an older person could cause a serious deficit in hydration level. It appears that older adults are under the impression that they must lose a large amount of fluid to become dehydrated, and they might not recognize that their specific medical conditions or medications could place them at a much higher risk for hydration-related issues. Furthermore, few respondents were familiar with the potentially serious or life-threatening consequences of dehydration. Less than one-third knew that seizures, or even death, can occur as a result of dehydration. Thus, these individuals may not adequately increase their fluid intake to cope with conditions that cause dehydration (e.g., vomiting or fever). It is also possible that caretakers or family members lack sufficient knowledge about the importance of hydration for the elderly and they may not urge the individual to drink more fluids or seek medical attention.

With respect to overhydration, few respondents understood its significance or recognized the signs and symptoms associated with it. Less than one-third were aware of the hazards of receiving intravenous fluids, blood transfusions, or steroids at an older age. Likewise, very few of the respondents knew that seizures, confusion, and death were potential complications of overhydration. Our data indicate that we must not only augment our efforts to educate older adults and their caretakers about dehydration, but we must do the same for overhydration.

Healthcare providers also need to work towards enhancing the knowledge base and health literacy of older adults regarding the close relationship of electrolytes and water. Although we do not expect non-medical personnel to acquire expertise in this complex area, the critical role of water in regulating sodium and its effect of morbidity and mortality needs to be emphasized. This might give individuals who view water consumption as relatively unimportant a new appreciation of the power of water and hydration for health. Studies have demonstrated the positive effect of education on improving thehydration status in children but such interventions have not been tried in the elderly [60].

### 4.2Limitations of study

Our study participants were largely educated, white, community-dwelling residents of Central Arkansas and hence our results cannot be extrapolated to the general population with greater ethnic diversity and/or lower socio-economic and educational status. We did not evaluate the cognition of participants or record fluid intake. Another issue is that people may not fully disclose their intake of certain fluids such as alcoholic beverages, or might not consider drinks such as fruit or vegetable juices as reportable sources of fluid intake. Additionally, we did not address the controversies regarding hydration in palliative care, or hospice patients. Most studies suggest that active attempts to hydrate terminally ill patients, especially intravenously, should be avoided because such efforts are futile and might actually cause more discomfort and medical complications [14, 61]. However, this is an evolving area in medicine that requires considerable education of patients and caregivers, as well as providers [62, 63].

### 4.3Future directions

Dehydration and overhydration are significant health issues for the elderly population. This study provided basic information about fluid intake of elderly individuals residing in the southern part of the United States and revealed that there are significant gaps in this population’s knowledge about proper hydration. We should spearhead public awareness campaigns aimed at improving the health literacy of this vulnerable population about hydration and also advocate for the implementation of programs that educate and train healthcare workers (e.g., caretakers or nursing home personnel) on this subject. Future studies should have objective records of hydration levels and correlate these with the participants’ health, medical problems, physical performance and quality of life.

## Conflicts of interest

The authors declare no conflicts of interest.

## ACKNOWLEDGMENTS

This study was supported in part by the Claude D. Pepper Older American Independence Center grant, National Institute on Aging (1P30AG28718) awarded to University of Arkansas for Medical Sciences. We thank Laura Gocio for her assistance with manuscript preparation.


text: 2 edited body edited Dec 9 '18 at 12:00 orthocresol♦ 42.8k77 gold badges133133 silver badges263263 bronze badges Formation of imines is usually a nucleophilic subsitution of oxigen with nitrogen. For this to happen, the oxigen usually must be bound beforehand as carbon-oxigen bond is quite strong. The most straightforward way is to use acidic catalysis. Most reactions that you referenced use acidic catalysis, though sometimes it isn't immediately apparent because they use solid catalyst such as molecular sieves a.k.a. H-form zeolites. A few use Lewis acids, such as $$\ce{Ti(OEt)4}$$. They still count as acids. The cases when no acid is used are not pure nucleophilic substitution. The reference you provided features various oxidative and other catalytic reactions, proceeding through different mechanism, that do not need acid, and a few reactions where reagent itself bears acidic function, like tosil isocionatetosyl isocyanate, that is a strong electrophile and can bind with oxigenoxygen on its own. TL;DR: the cases when acid apparently isn't used usually include it in non-obvious way. Other cases proceed through wild varying different mechanisms, usually involving oxidation. Formation of imines is usually a nucleophilic subsitution of oxigen with nitrogen. For this to happen, the oxigen usually must be bound beforehand as carbon-oxigen bond is quite strong. The most straightforward way is to use acidic catalysis. Most reactions that you referenced use acidic catalysis, though sometimes it isn't immediately apparent because they use solid catalyst such as molecular sieves a.k.a. H-form zeolites. A few use Lewis acids, such as $$\ce{Ti(OEt)4}$$. They still count as acids. The cases when no acid is used are not pure nucleophilic substitution. The reference you provided features various oxidative and other catalytic reactions, proceeding through different mechanism, that do not need acid, and a few reactions where reagent itself bears acidic function, like tosil isocionate, that is a strong electrophile and can bind with oxigen on its own. TL;DR: the cases when acid apparently isn't used usually include it in non-obvious way. Other cases proceed through wild varying different mechanisms, usually involving oxidation. Formation of imines is usually a nucleophilic subsitution of oxigen with nitrogen. For this to happen, the oxigen usually must be bound beforehand as carbon-oxigen bond is quite strong. The most straightforward way is to use acidic catalysis. Most reactions that you referenced use acidic catalysis, though sometimes it isn't immediately apparent because they use solid catalyst such as molecular sieves a.k.a. H-form zeolites. A few use Lewis acids, such as $$\ce{Ti(OEt)4}$$. They still count as acids. The cases when no acid is used are not pure nucleophilic substitution. The reference you provided features various oxidative and other catalytic reactions, proceeding through different mechanism, that do not need acid, and a few reactions where reagent itself bears acidic function, like tosyl isocyanate, that is a strong electrophile and can bind with oxygen on its own. TL;DR: the cases when acid apparently isn't used usually include it in non-obvious way. Other cases proceed through wild varying different mechanisms, usually involving oxidation. 1 answered Dec 9 '18 at 11:26 permeakra 18.7k11 gold badge4040 silver badges8787 bronze badges Formation of imines is usually a nucleophilic subsitution of oxigen with nitrogen. For this to happen, the oxigen usually must be bound beforehand as carbon-oxigen bond is quite strong. The most straightforward way is to use acidic catalysis. Most reactions that you referenced use acidic catalysis, though sometimes it isn't immediately apparent because they use solid catalyst such as molecular sieves a.k.a. H-form zeolites. A few use Lewis acids, such as $$\ce{Ti(OEt)4}$$. They still count as acids. The cases when no acid is used are not pure nucleophilic substitution. The reference you provided features various oxidative and other catalytic reactions, proceeding through different mechanism, that do not need acid, and a few reactions where reagent itself bears acidic function, like tosil isocionate, that is a strong electrophile and can bind with oxigen on its own. TL;DR: the cases when acid apparently isn't used usually include it in non-obvious way. Other cases proceed through wild varying different mechanisms, usually involving oxidation.