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

The calculator will find the variance of $1$, $3$, $6$, $5$, $8$, with steps shown.
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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, $s^{2} = \frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1} = \frac{\frac{146}{5}}{4} = \frac{73}{10}$.

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