Joseph A. Allen, PhD is a professor of industrial and organizational (I/O) psychology at the University of Utah. A discrete distribution is used to calculate the probability that a random variable will be exactly equal to some value. 0 P(X = x) 1 and P(X = x) =1 are two conditions that must be . What is the average value of a single roll of a fair eight-sided die? Probabilities for a Poisson probability distribution can be calculated using the Poisson probability function. Courses on Khan Academy are always 100% free. The positive square root of the variance is called the standard deviation . Note that \displaystyle P (x) P (x) represents the probability of x, where x is a value of the random variable X. The binomial probability distribution is associated with a binomial experiment. Continuous Distribution Calculator. He has a Master's in Statistics from Wake Forest University. Whole population variance calculation. work out exactly 2.1 times. The probability distribution for a discrete random variable X is a comprehensive set of each potential value of X, along with the likelihood that X will take that value in one trial of the experiment. So, for example, this is going to be, the first outcome here is zero, and we'll weight it by The standard deviation of X is given by. Creative Commons Attribution/Non-Commercial/Share-Alike. To make sure probabilities are calculated correctly, we need to know if certain values are included or not included. . So, this calculator can take care of simple math for you once you enter value-probability pairs into the table. Knock out the content thoroughly to know how to calculate expected value, its formula, and some basics you should beware of. Using this cumulative distribution function calculator is as easy as 1,2,3: 1. finite number of values, zero, one, two, three, or four. Chiron Origin & Greek Mythology | Who was Chiron? Let's add 'em all together. Let's now look at the one slightly more difficult wrinkle these problems can throw at us. In other words, discrete probability distributions are used to describe the probabilities . All other trademarks and copyrights are the property of their respective owners. Psychological Research & Experimental Design, All Teacher Certification Test Prep Courses, How to Calculate the Mean or Expected Value of a Discrete Random Variable. Because of this, we get a clean interpretation of the expected value of a discrete random variable. Learn how to find the mean, variance and standard deviation for a discrete random variable using the TI-Nspire. - [Instructor] So, I'm Example 6: Find the mean of the probability distribution. is the Greek letter mu, which is often used to denote the mean. You may see ads that are less relevant to you. discrete random variable. $1.20 + $0.25 + (-$0.30) + (-$0.40) = $0.75. copyright 2003-2022 Study.com. a probability of 0.25, plus three times 0.25. So, we get 0.15, plus .8, plus .75, plus .4, and let's say 0.4, 0.75, 0.8. All values of P (X) must sum to one. Unlike the sample mean of a group of observations, which gives each observation equal weight, the mean of a random variable weights each outcome x i according to its probability, p i.The common symbol for the mean (also known as the . Well, this isn't saying The reason the variance is not in the same units as the random variable is because its formula involves squaring the difference between x and the mean. Step 3 - Enter the value of x. The variance measures the variability in the values of the random variable. Probabilities for continuous probability distributions can be found using the Continuous Distribution Calculator. Step 2: Multiply each possible outcome by the probability it occurs. Use the formula for the mean of a discrete random variable X to answer the following problems: If 40% of all the students are taking four classes, and 60% of all the students are taking three classes, what is the mean (average) number of classes taken for this group of students? Now let's look at a pair of examples, one where the probability distribution is given in the problem, and one where a small amount of extra logic is needed. wait, hold on a second. What is expected value of a discrete random variable? The variance can be computed by adding three rows: x-, (x-)2 and (x-)2f(x). Also, draw the probability distribution. Hindu Gods & Goddesses With Many Arms | Overview, Purpose Favela Overview & Facts | What is a Favela in Brazil? How to Calculate the Parameters of a Discrete Random Variable. Probability density function, cumulative distribution function, mean and variance. The possible values of X are 18, 19, and 20, denoted x1, x2, and x3, respectively; their proportions (probabilities) are equal to 0.50, 0.25, and 0.25 (denoted p1, p2, and p3, respectively). Use the formula for the mean of a discrete random variable X to answer the following problems:
\n![\"image0.jpg\"/](\"https://www.dummies.com/wp-content/uploads/451473.image0.jpg\")
\nSample questions
\n- \n
If 40% of all the students are taking four classes, and 60% of all the students are taking three classes, what is the mean (average) number of classes taken for this group of students?
\nAnswer: 3.4
\nIn this case, X represents the number of classes. In essence, you can and should treat expected value, mean, and average as completely the same thing. this video is the notion of an expected value of a The most common of the continuous probability distributions is normal probability distribution. The standard deviation can be found by taking the square root of the variance. Use the formula for the mean of a discrete random variable X to answer the following problems: Common Core Math Grade 8 - Expressions & Equations: DSST Western Europe Since 1945: Study Guide & Test Prep, 8th Grade Physical Science: Enrichment Program, Anatomy & Physiology for Teachers: Professional Development, Study.com ACT® Reading Test Section: Prep & Practice. For the uniform probability distribution, the probability density function is given by f (x)= { 1 b a for a x b 0 elsewhere. Whether it's to pass that big test, qualify for that big promotion or even master that cooking technique; people who rely on dummies, rely on it to learn the critical skills and relevant information necessary for success. We can calculate the mean (or expected value) of a discrete random variable asthe weighted average of all the outcomes of that random variable based on their probabilities. This, right over here, Mean and Variance of Random Variables Mean The mean of a discrete random variable X is a weighted average of the possible values that the random variable can take. Population and sampled standard deviation calculator. Dummies helps everyone be more knowledgeable and confident in applying what they know. Enter all known values of X and P (X) into the form below and click the "Calculate" button to calculate the expected value of X. Click on the "Reset" to clear the results and enter new values. The variance of a discrete random variable is given by: 2 = Var ( X) = ( x i ) 2 f ( x i) The formula means that we take each value of x, subtract the expected value, square that value and multiply that value by its probability. A TI 84 is used. Step 1: Create a probability distribution for the variable, if not given to you. The differences are that in a hypergeometric distribution, the trials are not independent and the probability of success changes from trial to trial. four workouts in a week, that has a probability of 0.1, plus four times 0.1. And one way to think about it is, once we calculate the expected Step 3: Add the products from Step 2 together. 2 = Var ( X) = E [ ( X ) 2], where denotes the expected value of X. To calculate the mean of any probability distribution, we have to use the following formula: The formula for Mean or Expected Value of a probability distribution is as follows: = x * P (x) Where, x = Data value. Continuous distributions are probability distributions for continuous random variables. So, one times 0.15 is 0.15. going to be equal to 2.1. Discrete Random Variables: A quantity whose exact value varies probabilistically, and who can only take a specific set of values. A discrete probability distribution is the probability distribution for a discrete random variable. Define the random variable and the value of 'x'. The possible values of X are 18, 19, and 20, denoted x1, x2, and x3, respectively; their proportions (probabilities) are equal to 0.50, 0.25, and 0.25 (denoted p1, p2, and p3, respectively).
\nTo find the mean of X, or the average age of the students in the class, multiply each value, xi, by its probability, pi, and then add the products:
\n![\"image3.jpg\"/](\"https://www.dummies.com/wp-content/uploads/451476.image3.jpg\")
\n \n
If you need more practice on this and other topics from your statistics course, visit to purchase online access to 1,001 statistics practice problems! Now you might be saying, Get the result! Step 2: Multiply each possible outcome x by the probability it occurs P. I like to write these out as an extra row, below the probability distribution. So, we get all of this is Problem: A set of 10 microwave ovens includes 3 that are defective. If so, you have a discrete variable. Plus, the outcome three has This calculator can help you to calculate basic discrete random variable metrics: mean or expected value, variance, and standard deviation. Forbidden City Overview & Facts | What is the Forbidden Islam Origin & History | When was Islam Founded? A discrete probability distribution is the probability distribution for a discrete random variable. workouts, sometimes one, sometimes two, sometimes Everyone who receives the link will be able to view this calculation, Copyright PlanetCalc Version: Based on the fact that this is a "fair" die, we can say that each outcome should have the same probability of occurring. So, for example, the discrete random variable "the number of red shirts owned by a randomly selected citizen in your hometown" may have the following probability distribution. The simplest example of this method is the discrete uniform probability distribution. Read Write Spell can expect an average donation of $0.75 from a single play of this game. There is an easier form of this formula we can use. For a continuous probability distribution, probability is calculated by taking the area under the graph of the probability density function, written f (x). Another difference between the two is that for the binomial probability function, we use the probability of success, p. For the hypergeometric probability distribution, we use the number of successes, r, in the population, N. The expected value and variance are given by E(x) = n$\left(\frac{r}{N}\right)$ and Var(x) = n$\left(\frac{r}{N}\right) \left(1 - \frac{r}{N}\right) \left(\frac{N-n}{N-1}\right)$. If we multiply these by the outcomes themselves and add them together, mathematically, that's the same as actually running out that large number of trials and taking the average of the outcomes directly. Holt McDougal Modern Biology Chapter 46: Cirulatory and Genetics - Principles of Heredity: Tutoring Solution, Bacterial Skin and Wound Infections: Tutoring Solution, The Settlement of North America (1497-1732), Quiz & Worksheet - Practice with Semicolons, Quiz & Worksheet - Comparing Alliteration & Consonance. Calculation precision. It is computed using the formula =x P(x). value of this variable, of this random variable, that in a given week, that To compute this, we essentially just take the weighted sum of the various outcomes, and we weight them by the probabilities. The formula for the mean of a discrete random variable is given as follows: E[X] = x P(X = x) Discrete Probability Distribution Variance. Step 1 - Enter the minimum value a. We interpret expected value as the predicted average outcome if we looked at that random variable over an infinite number of trials. It's easiest to ask yourself "for any two quantities our variable can take, are there values in between our variable can't take?" negative probabilities, which wouldn't have made sense. We can help you track your performance, see where you need to study, and create customized problem sets to master your stats skills. By entering your email address and clicking the Submit button, you agree to the Terms of Use and Privacy Policy & to receive electronic communications from Dummies.com, which may include marketing promotions, news and updates. For these problems, let X be the number of classes taken by a college student in a semester. A third way is to provide a formula for the probability function. And you can see that this is a valid probability distribution because the combined probability is one. For these problems, let X be the number of classes taken by a colle","noIndex":0,"noFollow":0},"content":"
When working with random variables, you need to be able to calculate and interpret the mean. So, the units of the variance are in the units of the random variable squared. And so, we just have to The calculator will generate a step by step explanation along with the graphic representation of the data sets and regression line. The two weight based examples wouldn't work for this check then - you can be 150 pounds, or 160, or 155, or 154.7, or 155.9234923046582 pounds. Mean or expected value of discrete random variable is defined as. X P(x) 0 0.2 1 0.3 2 0.2 3 0.2 4 0.1 Select the current data in the table (if any) by clicking on the top checkbox and delete it by clicking on the "bin" icon on the table header. What is the expected value of the donation received by a single play of this game? .1 plus 0.15, plus 0.4, plus 0.25, plus 0.1 is one. discrete random variable, which we would just note this way. If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Plus, the next outcome is one, and it'd be weighted by Discrete random variables can be described using the expected value and variance. Answer each of the following: State the possible values that X can take. referred to as the mean of a random variable. We can calculate the mean (or expected value) of a discrete random variable as the weighted average of all the outcomes of that random variable based on their probabilities. A discrete random variable takes whole number values such 0, 1, 2 and so on while a continuous random variable can take any value inside of an interval. Defining the discrete random variable X as: X: the number obtained when we pick a ball at random from the bag and given that its probability distribution function is: P ( X = x) = 8 x x 2 40. In this case, X represents the age of a student. Different Strategies to Support Effective Reading. Sometimes you need to use them to solve probability theory problems. First, a "random variable" is a value that can change each time you measure it, depending on the specifics of how you measure it. Covariance Calculator. Two times 0.4 is 0.8. Calculate the probability of picking a ball with 2 on it. Click on the "import" icon on the table header and enter the following values. here are whole numbers. You can change your choice at any time on our, Binomial distribution, probability density function, cumulative distribution function, mean and variance, Hypergeometric Distribution. Learn how PLANETCALC and our partners collect and use data. A discrete probability distribution can be represented in a couple of different ways. But what we care about in Contact us by phone at (877)266-4919, or by mail at 100ViewStreet#202, MountainView, CA94041. Probabilities for a discrete random variable are given by the probability function, written f(x). Discrete Random Variables: A quantity whose exact value varies probabilistically, and who can only take a specific set of values. So, even for a random variable that can only take on integer values, you can still have a Another method is to create a graph with the values of x on the horizontal axis and the values of f(x) on the vertical axis. defining the random variable x as the number of workouts that Mitchell Tague has taught all levels of undergraduate statistics, among other math and science courses at the high school and college levels, for the past seven years. His articles have appeared in Human Relations, Journal of Business Psychology, and more.
Karin M. Reed is CEO of Speaker Dynamics, a corporate communications training firm. And none of these are Mean or expected value of discrete random variable is defined as, Variance of random variable is defined as, An alternative way to compute the variance is. The possible values of X are 4 and 3, denoted x1 and x2, respectively; their proportions (probabilities) are equal to 0.40 and 0.60 (denoted p1 and p2, respectively). This keeps things well organized. P (x) = Probability of value. The expectation or the mean of a discrete random variable is a weighted average of all possible values of the random variable. Second, a value is "discrete" if it can be broken down into a finite set of outcomes. The following are the simple steps to find the expected value or mean for the discrete probability . When working with random variables, you need to be able to calculate and interpret the mean. We interpret expected value as the predicted average outcome if we looked at that random variable over an infinite number of trials. Three times 0.25 is 0.75. A closely related topic in statistics is continuous probability distributions. "One of the following characters is used to separate data fields: tab, semicolon (;) or comma(,)" Sample: -50.5;? Question 1: Calculate the mean and variance for a random variable, X defined as the number of tails in four tosses of a coin. The probability distribution is given to us here, so we don't have to consider this. would give you a sense of the expected number of workouts. the random variable x. This is also sometimes Zero times anything is just zero. This means it is the sum of the squares of deviations from the mean. The possible values of X are 18, 19, and 20, denoted x1, x2, and x3, respectively; their proportions (probabilities) are equal to 0.50, 0.25, and 0.25 (denoted p1, p2, and p3, respectively).
\nTo find the mean of X, or the average age of the students in the class, multiply each value, xi, by its probability, pi, and then add the products:
\n\n \n\nIf you need more practice on this and other topics from your statistics course, visit to purchase online access to 1,001 statistics practice problems! Add value-probability pairs (you need to determine them, but it is the essence of the problem). - Definition & Examples, General Social Science and Humanities Lessons. Enter data values delimited with commas (e.g: 3,2,9,4) or spaces (e.g: 3 2 9 4) and press the Calculate button. Centeotl, Aztec God of Corn | Mythology, Facts & Importance. But this is valuable A binomial experiment consists of a sequence of n trials with two outcomes possible in each trial. Like the variance, the standard deviation is a measure of variability for a discrete random variable. And then this is two plus eight is 10, plus seven is 17, plus four is 21. Quiz & Worksheet - What is Guy Fawkes Night? Probability density function, cumulative distribution function, mean and variance, Poisson Distribution. Expected Value of Y / Mean of Y. Step 1: Determine the possible values for the random variable. 1 2 3. Probability Distribution: Discrete random variables are best described by probability distributions - for any given outcome, the probability that outcome in particular occurs is given. Instead, it should be interpreted as an average value if repeated shipments will be made under these conditions. An online expected value calculator helps to find the probability expected value (mean) of a discrete random variable (X). If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. 3.0.4170.0. The Variance is: Var (X) = x2p 2. The sum of all the possible probabilities is 1: P(x) = 1. Well, we can simplify this a little bit. When considering a discrete random variable, the probability of any individual outcome is the proportion of an aggressively large number of trials that that outcome is achieved. A Poisson experiment is one in which the probability of an occurrence is the same for any two intervals of the same length and occurrences are independent of each other. Step 2 - Enter the maximum value b. Remember that expected value calculation helps to reduce the information to one possibility/answer. The hypergeometric probabiity distribution is very similar to the binomial probability distributionn. These are sample statistics rather than the variances that would be calculated for abstract random variables. Another term often used to describe the mean is expected value. So, it's zero times 0.1. Probability distributions calculator. However, unlike the variance, it is in the same units as the random variable. Then sum all of those values. Step 4 - Click on "Calculate" button to get discrete uniform distribution probabilities. TExES Science of Teaching Reading (293): Practice & Study GACE School Counseling (603): Practice & Study Guide, American Literature Syllabus Resource & Lesson Plans. The Standard Deviation is: = Var (X) Question 1 Question 2 Question 3 Question 4 Question 5 Question 6 Question 7 Question 8 Question 9 Question 10. The possible values of X are 4 and 3, denoted x1 and x2, respectively; their proportions (probabilities) are equal to 0.40 and 0.60 (denoted p1 and p2, respectively).
\nTo find the average number of classes, or the mean of X, multiply each value, xi, by its probability, pi, and then add the products:
\n![\"image1.jpg\"/](\"https://www.dummies.com/wp-content/uploads/451474.image1.jpg\")
\nThe mean of X is denoted by
\n![\"image2.jpg\"/](\"https://www.dummies.com/wp-content/uploads/451475.image2.jpg\")
\n \n If half of the students in a class are age 18, one-quarter are age 19, and one-quarter are age 20, what is the average age of the students in the class?
\nAnswer: 18.75
\nIn this case, X represents the age of a student. Here are a few real-life examples that help to differentiate between discrete random variables and continuous random . Variance: The variance of a random variable is the standard deviation squared. When working with random variables, you need to be able to calculate and interpret the mean. So, one way to think about it is the expected value of x, the expected number of Now right over here, this table describes the Population mean: Population variance: Sampled data variance calculation. It is associated with a Poisson experiment. Standard deviation () calculator with mean value & variance online. We can calculate the mean . I will do in a given week. In words, the variance of a random variable is the average of the squared deviations of the random variable from its mean (expected . Here is the formula that we have come up with for the mean of a discrete random variable. These ads use cookies, but not for personalization. finite number of values here, we would call this a Enter a probability distribution table and this calculator will find the mean, standard deviation and variance. The possible values of X are 4 and 3, denoted x1 and x2, respectively; their proportions (probabilities) are equal to 0.40 and 0.60 (denoted p1 and p2, respectively).
\nTo find the average number of classes, or the mean of X, multiply each value, xi, by its probability, pi, and then add the products:
\n\nThe mean of X is denoted by
\n\n If half of the students in a class are age 18, one-quarter are age 19, and one-quarter are age 20, what is the average age of the students in the class?
\nAnswer: 18.75
\nIn this case, X represents the age of a student. Let's say [latex]x =[/latex . Example 4.2.1: two Fair Coins. Use the formula for the mean of a discrete random variable X to answer the following problems:
\n\nSample questions
\n- \n
If 40% of all the students are taking four classes, and 60% of all the students are taking three classes, what is the mean (average) number of classes taken for this group of students?
\nAnswer: 3.4
\nIn this case, X represents the number of classes. As you can see, these metrics have quite simple formulas. Choose a distribution. Of course, 1.5 defective ovens do not make any physical sense. You can find an example of usage below the calculator. ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8947"}}],"primaryCategoryTaxonomy":{"categoryId":33728,"title":"Statistics","slug":"statistics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33728"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[{"label":"Sample questions","target":"#tab1"}],"relatedArticles":{"fromBook":[{"articleId":207668,"title":"Statistics: 1001 Practice Problems For Dummies Cheat Sheet","slug":"1001-statistics-practice-problems-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207668"}},{"articleId":151951,"title":"Checking Out Statistical Symbols","slug":"checking-out-statistical-symbols","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/151951"}},{"articleId":151950,"title":"Terminology Used in Statistics","slug":"terminology-used-in-statistics","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/151950"}},{"articleId":151947,"title":"Breaking Down Statistical Formulas","slug":"breaking-down-statistical-formulas","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/151947"}},{"articleId":151934,"title":"Sticking to a Strategy When You Solve Statistics Problems","slug":"sticking-to-a-strategy-when-you-solve-statistics-problems","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/151934"}}],"fromCategory":[{"articleId":263501,"title":"10 Steps to a Better Math Grade with Statistics","slug":"10-steps-to-a-better-math-grade-with-statistics","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/263501"}},{"articleId":263495,"title":"Statistics and Histograms","slug":"statistics-and-histograms","categoryList":["academics-the-arts","math","statistics"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/263495"}},{"articleId":263492,"title":"What is Categorical Data and How is It Summarized? And so, because there's a The net donation from a single play of the game is given by the following probability distribution. An alternative way to compute the variance is. Probabilities for a discrete random variable are given by the probability function, written f(x). Expected Value: The mean, or average, of a set of numbers. Digital Marketing & Advertising: Assignment 2 - Digital What are the National Board for Professional Teaching How to Register for the National Board for Professional Statistical Discrete Probability Distributions, Problems with Algebraic Expressions and Equations. The variance of a random variable X is given by. Using the Casio fx-115es Plus to find the Mean and Standard Deviation of a Discrete Random Variable In this case, X represents the number of classes. The probability of x successes in n trials is given by the binomial probability function. Provide the outcomes of the random variable (X) (X), as well as the associated probabilities (p (X)) (p(X)), in the form below: X values (comma or space separated) =. This result does seem appropriate for a statistical system, but might not be the correct answer for a probability homework question. Sometimes I might do zero Step 2: The mean of the random variable X X is equal to =xP (X . It is a useful term because it reminds us that the mean of a random variable . Explanation, $ \text{Var}(x) = \sum (x - \mu)^2 f(x) $, $ f(x) = {n \choose x} p^x (1-p)^{(n-x)} $, $ f(x) = \dfrac{{r \choose x}{N-r \choose n-\cancel{x}}}{{N \choose n}} $. its probability of 0.15. What is .1 of a workout? For these problems, let X be the number of classes taken by a college student in a semester. Here is that calculation: . A discrete random variable takes whole number values such 0, 1, 2 and so on while a continuous random variable can take any value inside of an interval. This video tutorial shows how to use the TI-83 calculator to compute the mean and standard deviation of a discrete probability distribution. add up these numbers. Formula After that, you will get a mean of 1.5. And so, let's see, five plus five is 10. Expected Value of X / Mean of X. For discrete random variables, the trick is to find correct value-probability pairs; then, it is just simple math of additions and multiplications. Probabilities in general can be found using the Basic Probabality Calculator. its probability of 0.1. The expected value, or mean, measures the central location of the random variable. Note that the quickest way to do it is to "import" data. There are two pieces at play here to understanding these fully. All of the outcomes And as you can see, x can take on only a Step 5 - Gives the output probability at x for discrete uniform distribution. A random variable that takes on a finite or countably infinite number of values is called a Discrete Random Variable. If 5 of the ovens are chosen randomly for shipment to a hotel, how many defective ovens can they expect? There are two requirements for the probability function. Calculate and interpret the mean or expected value of a discrete random variable; Calculate the standard deviation of a discrete random variable; Recall: Translating Words to Inequality Statements. Quiz & Worksheet - Physical Geography of Australia, Quiz & Worksheet - Types of Persuasive Workplace Messages. Here, we have to create the probability distribution ourselves. So, this is the mean of And then four times .1 is 0.4. Digits after the decimal point: 2. To calculate the mean (that is the average), we have to add 30 fives + 52 tens + 62 fifteens + 40 twenties + 16 twenty-fives and then divide by 200. So, plus one times 0.15. non-integer expected value, and it is still useful. We can help you track your performance, see where you need to study, and create customized problem sets to master your stats skills.
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She is an Emmy award-winning broadcast journalist. The positive square root of the variance is called the standard deviation. Definition 3.5. {"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T08:26:52+00:00","modifiedTime":"2016-03-26T08:26:52+00:00","timestamp":"2022-09-14T17:54:12+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Statistics","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33728"},"slug":"statistics","categoryId":33728}],"title":"Determining the Mean of a Discrete Random Variable","strippedTitle":"determining the mean of a discrete random variable","slug":"determining-the-mean-of-a-discrete-random-variable","canonicalUrl":"","seo":{"metaDescription":"When working with random variables, you need to be able to calculate and interpret the mean. 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