# Variance and standard deviation of a discrete random variable | AP Statistics | Khan Academy | Summary and Q&A

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July 14, 2017
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Khan Academy
Variance and standard deviation of a discrete random variable | AP Statistics | Khan Academy

## TL;DR

This video explains how to calculate the variance and standard deviation of a discrete random variable, using the example of the number of workouts done in a week.

## Questions & Answers

### Q: How is the expected value of a discrete random variable calculated?

The expected value or mean is calculated by taking the probability-weighted sum of the various outcomes. It involves multiplying each outcome by its respective probability and summing them all up.

### Q: What is the formula for variance of a random variable?

The formula for variance involves taking the difference between each outcome and the mean, squaring that difference, and multiplying it by the probability of that outcome. These terms are then summed up to give the variance.

### Q: How is the standard deviation related to variance?

The standard deviation is obtained by taking the square root of the variance. It provides a measure of the spread or dispersion of the random variable's values around the mean.

### Q: Can the mean of a random variable be a non-integer value?

Yes, the mean of a random variable can be a non-integer value. This is because the mean is a weighted average of the possible outcomes, and the probabilities assigned to each outcome can result in a non-integer mean.

## Summary & Key Takeaways

• The video discusses the concept of expected value or mean of a discrete random variable, which is calculated by taking the probability-weighted sum of the various outcomes.

• The variance of a random variable is determined by taking the difference between each outcome and the mean, squaring that difference, and multiplying it by the probability of that outcome.

• The standard deviation is obtained by taking the square root of the variance.

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