# What is the variance of the following numbers?: {4,7,4,2,1,4,5}

Oct 23, 2015

3.27

#### Explanation:

Variance = $\sum {x}^{2} / n$ -${\left(m e a n\right)}^{2}$

Mean = $\sum \frac{x}{n}$ where n in the number of terms
= $\frac{4 + 7 + 4 + 2 + 1 + 4 + 5}{7}$
= $\frac{27}{7}$
= 3.857

$\sum {x}^{2}$ = ${4}^{2} + {7}^{2} + {4}^{2} + {2}^{2} + {1}^{2} + {4}^{2} + {5}^{2}$
= 127

SO Variance = $\frac{127}{7}$ - ${\left(3.857\right)}^{2}$
= 3.27