Question

If for a sample of size 60, we have the following information $\sum _{}{x}_i^2=18000$ and $\sum _{}{x}_i=960$, then the variance is

(a) 6.63 (b) 16 (c) 22 (d) 44

Answer 1

Given: $\sum _{}{x}_i^2=18000$, $\sum _{}{x}_i=960$ and n = 60

∴ Variance

$$\begin{gathered} =\frac{\sum _{}{x}_i^2}{n}-{\left(\frac{\sum _{}{x}_i}{n}\right)}^2 \\ =\frac{18000}{60}-{\left(\frac{960}{60}\right)}^2 \\ =300-256 \\ =44 \end{gathered}$$

Hence, the correct answer is option (d).