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1 min read•june 3, 2020

Kanya Shah

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

**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.

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.*

🎥**Watch: AP Stats - ****Probability: Random Variables, Binomial/Geometric Distributions**

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