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

May 26, 2016

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

#### Explanation:

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

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.
${\left(17 - 7.2857\right)}^{2} + {\left(3 - 7.2857\right)}^{2} + {\left(10 - 7.2857\right)}^{2} \setminus \cdots = 413.43$

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.
$\setminus {\sigma}^{2} = \setminus \frac{413.43}{7} = 59.061$ (Population)
${s}^{2} = \setminus \frac{413.43}{6} = 68.9051$ (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.