# Sample/Population Variance Calculator

For the given set of values, the calculator will find their variance (either sample or population), with steps shown.

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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 $$\left(2 - \frac{23}{10}\right)^{2} + \left(1 - \frac{23}{10}\right)^{2} + \left(9 - \frac{23}{10}\right)^{2} + \left(-3 - \frac{23}{10}\right)^{2} + \left(\frac{5}{2} - \frac{23}{10}\right)^{2} = \frac{374}{5}.$$$