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The following information relates to a sample of size 60: $\sum x^2 =18000, \sum x =960$ The variance is

$\begin{array}{1 1}(A)\; 6.63 \\(B)\;16 \\(C)\;22 \\(D)\; 44 \end{array}$

Can you answer this question?

Toolbox:
• The formula to calculate variance is $\sigma^2= \large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2$
Given $n=60$
$\sum x =960$
$\sum x^2 =18000$
$\sigma^2= \large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2$
$\qquad= \large\frac{18000}{60} - \bigg(\frac{ 960}{60}\bigg)^2$
$\qquad= 300- 16^2$
$\qquad= 300- 256$
$\qquad= 44$
Hence D is the correct answer.
answered Jul 9, 2014 by