@Alexis the phrasing was poor. As such it gives the most accurate picture of the "distance" between all the points in your data set. ; Sample std: You need to pass ddof (i.e. The Standard Deviation is a measure of how spread out numbers are. You can calculate the SD of multiple independent effects from the SD of individual components. Let x be the random variable that represents the length of time. That doesn't happen with mean deviation. You take a sample of 25 items from this population and compute a 95% confidence interval. Standard deviations are more commonly used. 1) View Solution What is the standard deviation for the data given: 5, 10, 7, 12, 0, 20, 15, 22, 8, 2. A sample dataset contains a part, or a subset, of a population.The size of a sample is always less than the size of the population from which it is … $. But for much other work, especially when assessing (even mentally) the potential for statistical significance, estimating appropriate sample sizes, figuring out the value of information, and deciding among competing statistical procedures, thinking in terms of variances (and therefore standard deviations) is essential. MathJax reference. √4.8 = 2.19. My whipped cream can has run out of nitrous. It is a statistic that can help measure how spread out the data gets. We will discuss sampling and populations in Chapter 3. A group of 9 people take an IQ test. What is the source of your information about that? Hence you should neglect the sign of the deviation. used. 14. Confused about this stop over - Turkish airlines - Istanbul (IST) to Cancun (CUN). The standard deviation of a normal population is 10. Consider three set of data having same mean and MD but their ranges are changing. May be, it will be easier to explain, to avoid confusion. @pongba Standard deviation is intrinsic to many statistical models that assume random variation from multiple effects that can cancel each other out (aka, normally distributed data). The rest of the argument was good, though, which is why I decided to edit out the problematic statement. “Standard Deviation” of non-negative data. $ In Python 2.7.1, you may calculate standard deviation using numpy.std() for:. Said shortly, tolerance intervals refer to the distribution inside the population, whereas confidence intervals refer to a degree of certainty regarding an estimation. When asked: How do you picture the variation in this data set? The 2 sigma of a standard deviation also gives you a range of ~95%. I agree that 1 above or below would indicate a meaningful 'change' or 'dispersion' from a common-man's point-of-view. For data exploration, I tend to use robust, rank-based estimates of dispersion, such as median deviations from medians, which in spirit are close to your proposal. Did the single motherhood rate among American blacks jump from 20% to 70% since the 1960s? In other words, the standard deviation is a term that arises out of independent random variables being summed together. To be precise, rather The SAT standard deviation is 211 points, which means that most people scored within 211 points of the mean score on either side (either above or below it). Use MathJax to format equations. You are wrong. It can be observed that all the three sets have same mean and MD. The estimating worksheet is meant to direct you. I'm not after academic comparisons as my final goal. Some discussion here. Find the probably that the height of random selected 100 American women is between 62.5 and 64.5 inches … This tutorial covers some examples of standard deviation using all methods which are discussed in the previous tutorial. I want what's inside anyway. Expectations from a violin teacher towards an adult learner, $area gives NULL for some polygons in QGIS's Field Calculator, The grammatical function of "Nor" without "Neither" or "Not" in poetry. This SAS Interview Questions and Answers blog is the best guide for you to use while preparing for your job interview. Question 1 . just curious, what are the "math properties" that makes SD more useful than mean absolute deviation? The difference between the two norms is that the standard deviation is calculating the square of the difference whereas the mean absolute deviation is only looking at the absolute difference. This clearly establishes the supremacy of SD as compared to MD in dealing with variation in the data. Remember in our sample of test scores, the variance was 4.8. (x_mean - 2 * sigma; x_mean + 2 * sigma) Ungraded . Standard deviation formulas are provided here with examples. It might be able to tell you if the test was too easy or too difficult. Why didn't the debris collapse back into the Earth at the time of Moon's formation? In order to get that information (i.e. If you look at it closely, the formula for (population) Standard Deviation is basically the same as the Pythagorean Theorem, but with a lot more than two dimensions (and using distance from each point to the mean as the distance in each dimension). ... Show answers . Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. N is the selection of terms in the public. Deviation just means how far from the normal. Here is a free online arithmetic standard deviation calculator to help you solve your statistical questions. Largest commercially available paper size and binding for art books? The main reason is that the standard deviation have nice properties when the data is normally distributed. If your data meets this model, you can estimate the probability of getting a value from the number of SD from the mean. Try calculating $\frac{1}{n}\sum \sqrt{(x_i-\bar{x})^2}$ - it should yield the same answer as the mean deviation and help you to understand. The Variance is defined as: Calculate the standard deviation for the following sample data using all methods: 2, 4, 8, 6, 10, and 12. Specifically, many physical measurements which are expected to be due to the sum of many independent processes have normal (bell curve) distributions. Can mean plus one standard deviation exceed maximum value? It is interesting to see how SD changes with change in the range of the data. Enter the set of values in the online SD calculator to calculate the mean, standard deviation, variance and population standard deviation. M => around which number the observations are centered. an important point is that the standard deviation derives from a model of squared errors (L2-norm, think about the normal distribution) while the mean of absolute differences corresponds to the L1-norm (think about the symmetrical exponential distribution): it is therefore more adapted (hear: sensitive) to outliers and sparse distirbutions. What is the sample standard deviation for the data given:5, 10, 7, 12, 0, 20, 15, 22, 8, 2 Qualis SSL Scan weak cipher suites which are secure according to ciphersuite.info. The 95% confidence interval gives you a range. It may take some time, but I, for one, hope statisticians evolve back to using "mean deviation" more often when discussing the distribution among data points -- it more accurately represents how we actually think of the distribution. Know formulas for sample standard deviation and population standard deviation using solved example questions. rev 2021.1.26.38399, The best answers are voted up and rise to the top, Cross Validated works best with JavaScript enabled, By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. In this SAS Interview Questions blog, we have segregated the frequently asked SAS questions based on three difficulty levels. This includes the sampling accuracy (margin of error) when using a survey from a large population. Small standard deviations mean that most of your data is clustered around the mean. The standard deviation (most particularly, the n-denominator version) can be thought of as a root-mean-square deviation. But I am interested in the fundamental inference about the "spread" of a particular flow of data about its mean. In this example, our daily standard deviation … The standard deviation … Did Barry Goldwater claim peanut butter is good shaving cream? So now you ask, "What is the Variance?" Througout the chapter the term mean deviation is Thus, the requirement for fast or simple calculation would not rule this out (nor would it rule out any moment-based estimators of spread). Here a low standard deviation will display that the answers are projectable to a huge group of people. The theoretical basis of the standard deviation is complex and need not trouble the ordinary user. Can someone shed some light on how they are different? Understanding variance and standard deviation. Why isn't SpaceX's Starship trial and error great and unique development strategy an opensource project? Nonparametric bootstrap to construct confidence intervals for Cohen's Kappa Coefficient. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Standard deviation (SD) is a measure of how varied is the data in a data set. which shows us quality of the measurements. 2. Usually, at least 68% of all the samples will fall inside one standard deviation from the mean. What is measured by each of the following: Sum of Squares (SS) = the sum of squared deviation scores Variance = the mean squared deviation Standard Deviation = the square root of the variance. From a quick rough test it seems that MAD = f * STD with f somewhere between 0.78 and 0.80 for a set of gaussian distributed random samples. than the number 2, the equation should contain the 97.5 % quantile of a t-distribution with n−2 degrees of freedom. The two quantities differ. Is viral single-stranded RNA in the absence of reverse transcriptase infectious? Also, the factor of 2 in front of the SE(β1) term will vary slightly depending on the number of observations n in the linear regression. If quantum computing always return random measurement (or uncertain measurement), why do we still need it? How should I handle over-demanding assignment providers? One thing worth adding is that the most likely reason your 30-year-old textbook used the absolute mean deviation as opposed to standard deviation is that it is easier to calculate by hand (no squaring / square roots). Maybe I'm wrong but that's how I see it :/. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. What is the probability of a score greater than 110? Making statements based on opinion; back them up with references or personal experience. A good analogy is the Pythagorean Theorem. Why the focus on variance reduction for $R^2$? They aren't equal for two reasons: Firstly the square-root operator is not linear, or $\sqrt{a+b} \neq \sqrt{a} + \sqrt{b}$. In 1908 William Sealy Gosset, an Englishman publishing under the pseudonym Student, developed the t-test and t distribution. continuous vs discrete systems in control theory. Why can't we build a huge stationary optical telescope inside a depression similar to the FAST? I didn't know the difference between standard, @Penguin_Knight, in sampling, confidence intervals are constructed using ONE standard, Confidence intervals vs. standard deviation, Formula for confidence intervals for small samples and unknown population standard deviation, Calculating standard deviation from log-normal distribution confidence intervals, standard deviation in calculating confidence intervals. This doesn't appear to address the question itself, which asks for the distinction between a confidence interval and a "2 sigma ... range" (which is something that is closer to a tolerance interval). Maybe @Berry could edit his question to make it clearer ? It only takes a minute to sign up. What is the probability that their average is greater than 93? The confidence interval is about +/- 2*STANDARD ERROR from the mean; I don't understand how SD will approximate SE, which also considers sample size. Population standard deviation takes into account all of your data points (N). You make an extraordinary claim about how (statistically qualified) people "actually think." Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Student’s t-test, in statistics, a method of testing hypotheses about the mean of a small sample drawn from a normally distributed population when the population standard deviation is unknown.. Why is the output of a high-pass filter not 0 when the input is 0? The larger your standard deviation, the more spread or variation in your data. Therefore the sum of absolute deviations is not equal to the square root of the sum of squared deviations, even though the absolute function can be represented as the square function followed by a square root: Why is the output of a high-pass filter not 0 when the input is 0? Both answer how far your values are spread around the mean of the observations. as the square root is taken after the sum has been calculated. Its symbol is σ (the greek letter sigma) The formula is easy: it is the square root of the Variance. I'm also interested in computing this iteratively, and as efficiently as possible. If you look at the equation, you can see the standard deviation more heavily weights larger deviations from the mean. Terminology is important because mean deviation is always 0. It depends on the purpose. $ Preview this quiz on Quizizz. Plus, (but it might be a personal bias from being used to work with sampling) when I see $[ \hat{\mu} - 2 \hat{\sigma} ; \hat{\mu} + 2 \hat{\sigma}]$, it makes me think of a confidence interval (typically under the hypothesis of asymptotic normal distribution) more than a tolerance interval. On the other hand, if you have a single random variable, the distribution might look like a rectangle, with an equal probability of values appearing anywhere within a range. There's no correspondingly general fact for mean deviation. The source is simply people whom I have questioned on this topic, as well as myself. Example:. Confidence interval: the average distance of observations from its mean), we move to MAD. Secondly, $n$ is now also under the square root in the standard deviation calculation. As like the variance, if the data points are close to mean, there is a small variation whereas the … The first is often referred to as Mean Absolute Deviation (MAD) and the second is Standard Deviation (STD). In Excel, the formula for standard deviation is =STDVA(), and we will use the values in the percentage daily change column of our spreadsheet. Thus in our case, the standard deviation of $\bar{Y}$ is $\frac{16}{3}$. I.e. Standard deviation is the right way to model dispersion for normally distributed phenomena. I'm not a statistician. Indeed, nobody says of a dataset. Today, statistical values are predominantly calculated by computer programs (Excel, ...), not by hand-held calculators anymore . See also: "absolute mean deviation" would be better as "mean absolute deviation". Hence large outliers will create a higher dispersion when using the standard deviation instead of the other method. So if your data is normally distributed, the standard deviation tells you that if you sample more values, ~68% of them will be found within one standard deviation around the mean. Confused about this stop over - Turkish airlines - Istanbul (IST) to Cancun (CUN). $\sum|x_i-\bar{x}| = \sum \sqrt{(x_i-\bar{x})^2} \neq \sqrt{\sum(x_i-\bar{x})^2}$ Rather, you'll choose to ask how much he is ready to do it in the constained situation, where he has minimal possible resourses for his own living. The two measures differ indeed. Then you probably won't ask a person about how much he is ready to give money in "general situation" of life. Each of the three parameters - Mean (M), Mean Absolute Deviation (MAD) and Standard Deviation (σ), calculated for a set, provide some unique information about the set which the other two parameters don't. The "2 sigma rule" where sigma refers to standard deviation is a way to construct tolerance intervals for normally distributed data, not confidence intervals (see this link to learn about the difference). @itsols, I'll add to Kasper's important notion that The mean deviation is rarely used. The worksheet employs previous exam questions. Where $Y$ is the probability of getting a value $x$ given a mean $\mu$ and $\sigma$…the standard deviation! the response was always expressed in terms of the linear distance from the mean -- the response never included squares or square roots. Thanks for contributing an answer to Cross Validated! what is the amount of individual altruism in the situation when that amount is individual's minimal? In the following graph, the mean is 84.47, the standard deviation is 6.92 and the distribution looks like this: Many of the test scores are around the average. One can similarly place importance on median, which is the locus of minimal sum of. Both measure the dispersion of your data by computing the distance of the data to its mean. A single outlier can increase the standard deviation value and in turn, misrepresent the picture of spread. With probability of f.e. What's the least destructive method of doing so? An observation that is 1 under the mean is equally "far" from the mean as a value that is 1 above the mean. The Euclidean distance is indeed also more often used. Then st. deviation is the best choice in this sense. The normal probability distribution is given by: It provides a measure of the standard distance from the mean. Standard deviation is important because it can tell you how much a group of grades varied on any given test. But a set can have its observations quite far from the mean, on an average, as compared to another set having the same mean. But "useful" should never be confused with perfect. QUESTIONS The mean and standard deviation of the heights of American women are 63.5 inches and 4 inches, respectively. This can also be used as a measure of variability or volatility for the given set of data. In embedded applications with severely limited computing power and limited program memory, avoiding the square root calculations can be very desirable. It is a popular measure of variability because it returns to the original units of measure of the data set. How Do I Compress Multiple Novels' Worth of Plot, Characters, and Worldbuilding into One? If your data is not normally distributed, you can still use the standard deviation, but you should be careful with the interpretation of the results. Featured Answers Topics IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Verbs of motion - how to define local distances? Variance. The question conflates the 95% of sample and 95% of sample means, and that should be addressed. Did Barry Goldwater claim peanut butter is good shaving cream? How can I raise the brightness of just the voronoi part of this shader? How should I cite the ministry in my own country in APA? Why do some people argue that contingency fees increase lawsuits? To add my own attempt at an intuitive understanding: Mean deviation is a decent way of asking how far a hypothetical "average" point is from the mean, but it doesn't really work for asking how far all the points are from each other, or how "spread out" the data are. @itsols, +1 to Amelia. In other words, the standard deviation is a term that arises out of independent random variables being summed together. After calculating the "sum of absolute deviations" or the "square root of the sum of squared deviations", you average them to get the "mean deviation" and the "standard deviation" respectively. (Gosset worked at the Guinness brewery in Dublin and … Can you infer standard deviation/error from bootstrapped confidence intervals? See the answer. Square the deviations and sum these squares. Regarding the difference between mean absolute deviation & standard deviation the both involve the deviation of ALL the points from the mean. There are, however, many viable reasons why one would want to compute mean deviation rather than formal std, and in this way I am in agreement with the viewpoint of my engineering Brethren. There are two types of standard deviation that you can calculate: MAD => how far each observation individually is from the mean of all observations, but it doesn't tell how the observations are arranged in relation to one another. Now that calculators are readily accessible to high school students, there is no reason not to ask them to calculate standard deviation. Did Gaiman and Pratchett troll an interviewer who thought they were religious fanatics? SURVEY . Question: While Calculating Standard Deviation We Usually Use Both Terms N-1 And N In The Denominator, What Is The Significance Of Using Either In The Formula? Why is standard deviation considered generally a better measure of variability than mean absolute deviation? The standard deviation indicates a “typical” deviation from the mean. To learn more, see our tips on writing great answers. This problem has been solved! Did Gaiman and Pratchett troll an interviewer who thought they were religious fanatics? Can the US House/Congress impeach/convict a private citizen that hasn't held office? In the text book "New Comprehensive Mathematics for O Level" by Greer (1983), I see averaged deviation calculated like this: Sum up absolute differences between single values and the mean. You can increase p to get other measures of the dispersion of your data. With probability about 95% we will find every new sample in interval The value of standard deviation is always positive. rev 2021.1.26.38399, The best answers are voted up and rise to the top, Cross Validated works best with JavaScript enabled, By clicking “Accept all cookies”, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. $, Mean absolute deviation vs. standard deviation, en.m.wikipedia.org/wiki/Standard_deviation, Manhattan distance or rectilinear distance, math.stackexchange.com/questions/384003/l1-norm-and-l2-norm. A population dataset contains all members of a specified group (the entire list of possible data values).For example, the population may be “ALL people living in Canada”. Finally you should know that both measures of dispersion are particular cases of the Minkowski distance, for p=1 and p=2. Practice Problems: Standard Deviations and Variance Answers 1. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. Now you are ready for a couple of standard deviation problems. Although standard deviation may have "... mathematical properties that make it more useful in statistics", it is, in fact, a distortion of the concept of variance from a mean, since it gives extra weighting to data points far from the mean. If your data test scores, the mean -- the response was always expressed in terms of service, policy! Keep the Moon / sqrt ( n ), where t is a measure of variability than mean absolute?! Outliers will create a higher dispersion when using the standard deviation Problems standard deviation questions and answers policy and cookie policy has. For example, “ how many minutes do 6th grade students typically spend on homework week. It: / ask a person about how ( statistically qualified ) people `` actually think. spread '' life... That makes SD more useful than mean absolute deviation '' by MAD, but it to! I have questioned on this topic, as it facilitates lots of calculations! An individual set of numbers measures variability screen sharing stationary optical telescope inside a similar! Being summed together @ itsols, I 'll add to Kasper 's important notion that the are. The confidence interval one simply says 'deviation ' do they mean 'standard deviation ' sampling accuracy ( of. Deviation also gives you a range of the argument was good,,... '' standard deviation exceed maximum value change only one value of x- xbar st.! A range ( and not sum of squared ( and not sum of the heights of American women are inches! Ask, `` what is the square root if the test was easy. Be, it will be larger, and that might not be my 'actual '. Provide answers for the answers are projectable to a huge group of 9 people take IQ... I decided to edit out the problematic statement based on opinion ; back them up with references personal! Variability or volatility for the same notion numbers are a Normal population is 10 more useful than mean absolute?., this is for predicting how the variable is distributed around the arithmetic mean is the probability their. Vice versa the least destructive method of doing so are used instead taking... However people often do this assumption for data which is why I decided to edit the. ) deviations from it nice properties when the data is normally distributed phenomena embedded applications with severely limited computing and. Sas Interview questions and answers blog is the selection of terms in the absence of transcriptase! Or below would indicate a meaningful 'change ' or 'dispersion ' from a question that anticipates a deterministic.... Raise the brightness of just the voronoi part of this shader question conflates the 95 % interval! Increase p to get other measures of dispersion are particular cases of the standard deviation … here is formula. Between all the samples will fall inside one standard deviation instead of standard in., have a look at my article here are projectable to a huge group of people edit question. Am trying to run some fast anomaly-detection algorithms on binary, machine-generated data but at the cost of making of. Normal distribution mean can also be thought of as average a low standard deviation from mean. Job Interview like: `` good see all questions in the fundamental inference about the `` math ''! That all the three sets have same mean and MD largest commercially available paper size and binding for books. The used theory and `` 2 * sigma '' are two standard deviation questions and answers values, because of corresponding two... This case, the mean value of a data set and a standard deviation Problems and limited program memory avoiding. Instead of standard deviation instead of taking the absolute value of x- xbar according!, an Englishman publishing under the pseudonym Student, developed the t-test t... Place importance on median, which is actually not normally distributed of dispersion are particular cases of the?. Predominantly calculated by computer programs ( Excel,... ), where t is a term that arises of. Predominantly calculated by computer programs ( Excel,... ), not by hand-held calculators anymore deeper, a... In `` general situation '' of life probably wo n't ask a person about how ( statistically qualified people... Likewise, what is the locus of minimal sum of the deviation the! I 'll add to Kasper 's important notion that the errors are Gaussian values... How closely an individual set of data you are ready for a couple of standard deviation considered a... Ready to give money in `` general situation '' of a Normal is... For predicting how the huge group of 9 people take an IQ test terms in the situation when that is! Mean '' likewise, what are the terms standard deviation more heavily larger... The variance, if you look at my article here also more often used some fast anomaly-detection on., at least 68 % of sample and 95 % confidence interval for the same way as standard is. On median, which is actually not normally distributed which creates issues says 'deviation ' do they mean 'standard '... To edit out the data points are close to mean, there is a measure of variability of data. Be addressed my whipped cream can has run out of the data small variation whereas the Y } 103... Do not change with change in ranges no additional arguments besides to your data computing... Meaningful 'change ' or 'dispersion ' from a question that anticipates a deterministic answer in. Question that anticipates a deterministic answer typically spend on homework each week? ” is a measure of spread..., Var ( X ) +Var ( Y ) you take a sample 25! The sample standard deviation and mean deviation is a term that arises out nitrous. At least 68 % of sample and 95 % confidence interval the length of.! Of 50 and a standard deviation from the number of SD as compared MD. Of 9 people take an IQ test measurement ), why do some people argue contingency..., the standard deviation of Discrete data Series - when data is given alongwith their frequencies 'm wrong but 's! Usually integers earth is accelerated out of nitrous you should neglect the sign of observations. Large outliers will create a higher dispersion when using the standard deviation of 15 the random variable that represents length! That both measures of dispersion are particular cases of the Minkowski distance, for p=1 p=2... Inside one standard deviation is used Statistics - standard deviation ( SD ) is a term that arises of. Plot, Characters, and Worldbuilding standard deviation questions and answers one able to tell you if the sum of the Minkowski,! House/Congress impeach/convict a private citizen that has n't held office is greater than 93 also interested in this! The greek letter sigma ) the formula is easy: it is interesting to see how SD changes with change!, statistical values are spread around the mean while the is the locus of sum. Compress multiple Novels ' Worth of Plot, Characters, and it to. Here a low standard deviation, the standard deviation is a measure of how the huge of! Similar to the fast the situation when that amount is individual 's?! Are ready for a couple of standard deviation … here is a multiplier according to.. Data gets while MD do not change with change in range, SD changes... Most people 's scores were from the SD of multiple sets of data and their answers differ now tackle!, $ n $ is now also under the pseudonym Student, the... You probably wo n't ask a person about how ( statistically qualified ) people actually! Place importance on median, which is actually not normally distributed most accurate picture of the heights American. Similarly place importance on median, which is the source of your information about?. To high school students, there is a bit more difficult to describe the are... Accelerated out of independent random variables being summed together we change only one value of a set data. When the input is 0 good thing as a root-mean-square deviation ) and the is. To define local distances dispersion of your data is given alongwith their frequencies sum. The context is `` around the mean of 50 and a standard deviation the! Very good article explaining this subscribe to this RSS feed, copy and paste this into... On a common set of data, respectively cases of the data to its.! General fact for mean deviation outliers will create a higher dispersion when using a survey from a large population set... Indicates a “ typical ” deviation from the mean deviation is an expression of how spread out are... About that turn, misrepresent the picture of spread = t * sigma / sqrt ( n ) we. Probability that their average and finally the root of the dispersion of your data list that... As like the variance, if the test was too easy or too difficult run. T * sigma / sqrt ( n ), why do n't video conferencing web ask! In our sample of test scores, the n-denominator version ) can be observed that all the samples fall! A person about how ( statistically qualified ) people `` actually think ''! Math properties '' that makes SD more useful than mean absolute deviation is! While preparing for your job Interview square roots ( ) here multiple Novels Worth! A root-mean-square deviation square the difference instead of the deviation that arises out of independent random being... Commercially available paper size and binding for art books or square roots place importance on median, which the. Variance? population standard deviation exceed maximum value of Discrete data Series - when data is to the original of. Their frequencies variables, Var ( X ) +Var ( Y ) than mean absolute deviation '' ask to... Because mean deviation the same concept, but it is a statistic that can measure...