Variance of $$$8$$$, $$$7$$$, $$$-2$$$, $$$6$$$, $$$3$$$, $$$2$$$
Your Input
Find the sample variance of $$$8$$$, $$$7$$$, $$$-2$$$, $$$6$$$, $$$3$$$, $$$2$$$.
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 $$$\mu = 4$$$ (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, $$$s^{2} = \frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1} = \frac{70}{5} = 14$$$.
Answer
The sample variance is $$$s^{2} = 14$$$A.