Question

What is the variance of {17, 3, 10, 1, -3, 4, 19}?

Answer 1

Population variance = 59.1 (probably what you want if this is an introductory class)
Sample variance = 68.9

Explanation:

Calculate the mean
`\frac{17 + 3 + 10 + 1 - 3 + 4 + 19}{7} = 7.2857`

Find the mean of the squared differences. To do this:
Square the difference between each data point and the mean. Add all of these squared differences.
`(17-7.2857)^2 + (3-7.2857)^2 + (10 - 7.2857)^2\cdots = 413.43`

If you're finding the population variance, divide by number of data points. If you're finding the sample variance, divide by the number of data points - 1.
`\sigma^2 = \frac{413.43}{7} = 59.061` (Population)
`s^2 = \frac{413.43}{6} = 68.9051` (Sample)

Round in whatever way you've been told to.

*If these are all the data points in the set, i.e. represent the entire population of data points, use the population variance.

If these data points are a sample of the data, i.e. there is a lot of data you're missing, but you want an accurate calculation for all of the data, use sample variance.

This WikiHow page has a detailed explanation for how to calculate the population and sample variance, with examples of when each would be appropriate.