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Sample/Population Variance Calculator
Calculate sample/population variance step by step
For the given set of values, the calculator will find their variance (either sample or population), with steps shown.
Your Input
Find the sample variance of $$$2$$$, $$$1$$$, $$$9$$$, $$$-3$$$, $$$\frac{5}{2}$$$.
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 $$$\mu = \frac{23}{10}$$$ (for calculating it, see mean calculator).
Since we have $$$n$$$ points, $$$n = 5$$$.
The sum of $$$\left(x_{i} - \mu\right)^{2}$$$ is $$$\left(2 - \frac{23}{10}\right)^{2} + \left(1 - \frac{23}{10}\right)^{2} + \left(9 - \frac{23}{10}\right)^{2} + \left(-3 - \frac{23}{10}\right)^{2} + \left(\frac{5}{2} - \frac{23}{10}\right)^{2} = \frac{374}{5}.$$$
Thus, $$$s^{2} = \frac{\sum_{i=1}^{n} \left(x_{i} - \mu\right)^{2}}{n - 1} = \frac{\frac{374}{5}}{4} = \frac{187}{10}$$$.
Answer
The sample variance is $$$s^{2} = \frac{187}{10} = 18.7$$$A.