# What is the variance of {1000, 600, 800, 1000}?

Jun 28, 2016

Variance is $27500$

#### Explanation:

The mean of data set is given by the sum of data divided by their number i.e. $\frac{\Sigma x}{N}$

Hence mean is $\frac{1}{4} \left(1000 + 600 + 800 + 1000\right) = \frac{3400}{4} = 850$

Variance is given by $\frac{\Sigma {x}^{2}}{N} - {\left(\frac{\Sigma x}{N}\right)}^{2}$

$\frac{\Sigma {x}^{2}}{N} = \frac{1}{4} \left({1000}^{2} + {600}^{2} + {800}^{2} + {1000}^{2}\right)$

= $\frac{1}{4} \left(1000000 + 360000 + 640000 + 1000000\right) = \frac{300000}{4} = 750000$

Hence variance is $750000 - {\left(850\right)}^{2} = 750000 - 722500 = 27500$