# Variance of $$$1$$$, $$$3$$$, $$$6$$$, $$$5$$$, $$$8$$$

### Your Input

**Find the sample variance of $$$1$$$, $$$3$$$, $$$6$$$, $$$5$$$, $$$8$$$.**

### Solution

The sample variance of data is given by the formula $$$s^{2} = \frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1}$$$, where $$$n$$$ is the number of values, $$$x_i, i=\overline{1..n}$$$ are the values themselves, and $$$\mu$$$ is the mean of the values.

Actually, it is the square of standard deviation.

The mean of the data is $$$\mu = \frac{23}{5}$$$ (for calculating it, see mean calculator).

Since we have $$$n$$$ points, $$$n = 5$$$.

The sum of $$$\left(x_{i} - \mu\right)^{2}$$$ is $$$\left(1 - \frac{23}{5}\right)^{2} + \left(3 - \frac{23}{5}\right)^{2} + \left(6 - \frac{23}{5}\right)^{2} + \left(5 - \frac{23}{5}\right)^{2} + \left(8 - \frac{23}{5}\right)^{2} = \frac{146}{5}$$$.

Thus, $$$s^{2} = \frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1} = \frac{\frac{146}{5}}{4} = \frac{73}{10}$$$.

### Answer

**The sample variance is $$$s^{2} = \frac{73}{10} = 7.3$$$A.**