Sample variance formula

In the video, you learned the following simple formula for variance:

$$\frac{\sum (X - M)^2}{N}$$

In practice, we'll often divide by $N-1$ rather than $N$ for reasons that are beyond the scope of this course. For now, just know that it's called the population variance when you use $N$ and the sample variance when using $N-1$ and you'll almost always use the sample variance when working with real data. Here's the formula for sample variance:

$$\frac{\sum (X - M)^2}{N - 1}$$

In this example, we have collected a sample of incomes for three people: $100, $300, and $500. Which of the following formulas would you use to calculate the variance of these incomes?

Possible answers

$\frac{((100-300)+(300-300)+(500-300))^2}{3-1}$

$\frac{(100-300)^2 + (300-300)^2 + (500-300)^2}{3-1}$

$\frac{(100-300)^2 + (300-300)^2 + (500-300)^2}{3}$

$\sqrt{\frac{(100-300)^2 + (300-300)^2 + (500-300)^2}{3-1}}$

Exercise

Sample variance formula

Instructions

Possible answers