# Standard deviation of $$$8$$$, $$$7$$$, $$$-2$$$, $$$6$$$, $$$3$$$, $$$2$$$

### Your Input

**Find the sample standard deviation of $$$8$$$, $$$7$$$, $$$-2$$$, $$$6$$$, $$$3$$$, $$$2$$$.**

### Solution

The sample standard deviation of data is given by the formula $$$s = \sqrt{\frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1}}$$$, 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 root of variance.

The mean of the data is $$$\mu = 4$$$ (for calculating it, see mean calculator).

Since we have $$$n$$$ points, $$$n = 6$$$.

The sum of $$$\left(x_{i} - \mu\right)^{2}$$$ is $$$\left(8 - 4\right)^{2} + \left(7 - 4\right)^{2} + \left(-2 - 4\right)^{2} + \left(6 - 4\right)^{2} + \left(3 - 4\right)^{2} + \left(2 - 4\right)^{2} = 70$$$.

Thus, $$$\frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1} = \frac{70}{5} = 14$$$.

Finally, $$$s = \sqrt{\frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1}} = \sqrt{14}$$$.

### Answer

**The sample standard deviation is $$$s = \sqrt{14}\approx 3.741657386773941$$$A.**