Mean and Variance

QAFE Framework

Question & Answer

1. What is Variance
   • How dispersed/measure of how spread a set of numbers are from their average value
2. Why is it useful?
   • Quantifying and observing for deviations within the data. Can attempt to identify how the variables differ.

Formula

1. Expected value of a random variable/average outcome Mean or expected value of a random variable $E(X)$ or $\mu$ measures the average outcome

$$\mu =E(X)=\sum xPr(X=x)$$

2. Variance of the random variable Standard deviation is the square root of the variance. SD is the measure of variability or volatility in the random variable

$${\sigma }^2=Var(X)=\sum (x-\mu {)}^{2}Pr(X=x)$$

Examples

Tossing a die