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AP Stats



Unit 4

4.8 Mean and Standard Deviation of Random Variables

1 min readjune 3, 2020

Kanya Shah

The main takeaway from this section should be knowing how to calculate and interpret the standard deviation and mean. 

Center of a Discrete Random Variable

Mean or Expected value of a discrete variable is its average value over many, many repetitions of the same chance process. To find the mean or expected value of X, multiply each possible value of X by its probability and then add all of the products.
The mean is the balance point of a distribution. Formula: Summation(xi*pi)= mean of X
Critical Tip: DO NOT write the mean of a random variable as a non integer value if it is a decimal because almost all expected values are decimals. 

Variability of a Discrete Random Variable

The standard deviation of a discrete random variable measures how much the values of the variable typically vary from the mean.
The variance of X is SD^2= summation(xi-mean of x)^2 * pi .
The standard deviation of X is the square root of the variance so SD = sqrt(summation(xi-mean of x)^2 * pi)
If you decide to use your calculator, make sure you list how you got to your answer. Use context and don’t just put a number down as the answer. Show work to maximize the amount of points you get.


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Unit 1: Exploring One-Variable Data
Unit 2: Exploring Two-Variable Data
Unit 3: Collecting Data
Unit 5: Sampling Distributions
Unit 6: Inference for Categorical Data: Proportions
Unit 7: Inference for Qualitative Data: Means
Unit 8: Inference for Categorical Data: Chi-Square
Unit 9: Inference for Quantitative Data: Slopes
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