# Variance of $$$1$$$, $$$37$$$, $$$9$$$, $$$0$$$, $$$- \frac{3}{5}$$$, $$$9$$$, $$$10$$$

### Your Input

**Find the sample variance of $$$1$$$, $$$37$$$, $$$9$$$, $$$0$$$, $$$- \frac{3}{5}$$$, $$$9$$$, $$$10$$$.**

### 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 $$$\mu = \frac{327}{35}$$$ (for calculating it, see mean calculator).

Since we have $$$n$$$ points, $$$n = 7$$$.

The sum of $$$\left(x_{i} - \mu\right)^{2}$$$ is $$$\left(1 - \frac{327}{35}\right)^{2} + \left(37 - \frac{327}{35}\right)^{2} + \left(9 - \frac{327}{35}\right)^{2} + \left(0 - \frac{327}{35}\right)^{2} + \left(- \frac{3}{5} - \frac{327}{35}\right)^{2} + \left(9 - \frac{327}{35}\right)^{2} + \left(10 - \frac{327}{35}\right)^{2} = \frac{178734}{175}.$$$

Thus, $$$s^{2} = \frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1} = \frac{\frac{178734}{175}}{6} = \frac{29789}{175}$$$.

### Answer

**The sample variance is $$$s^{2} = \frac{29789}{175}\approx 170.222857142857143$$$A.**