Exercise

# 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?

Instructions

**50 XP**

##### Possible Answers

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