# How do you find the sample variance in 89, 57, 104, 73, 26, 121, 81?

Dec 11, 2017

$970.2$

#### Explanation:

Dec 11, 2017

Use the formula for Variance of a Sample (not a Population).
${s}^{2} = \left(\frac{1}{N - 1}\right) {\sum}_{i = 1}^{N} {\left({x}_{i} - \overline{x}\right)}^{2}$

#### Explanation:

Many calculators, spreadsheets and even on-line calculators are available. It IS prudent to understand how to calculate it manually in every case! The formula for Variance of a Sample is:

${s}^{2} = \left(\frac{1}{N - 1}\right) {\sum}_{i = 1}^{N} {\left({x}_{i} - \overline{x}\right)}^{2}$

The Mean ($\overline{x}$) is $78.71$. The sum of the difference between it and the data values is divided by 1 less than the number of data for a sample.

In this case it is $970.2$ Its square root is the Standard Deviation, which is $31.1$.

https://www.rapidtables.com/calc/math/variance-calculator.html