7.4.4 Statistics, SPM Paper 1 (Short Questions)

Question 7:
A set of data consists of twelve positive numbers.

It is given that Σ {(x - \bar{x})}^{2} = 600 and Σ x^{2} = 1032.

Find
(a) the variance
(b) the mean

Solution:
(a)

\begin{array}{l} Variance = \frac{Σ {(x - \bar{x})}^{2}}{N} \\ = \frac{600}{12} \\ = 50 \end{array}

(b)

\begin{array}{l} Variance = \frac{Σ x^{2}}{N} - {(\bar{x})}^{2} \\ 50 = \frac{1032}{12} - {(\bar{x})}^{2} \\ {(\bar{x})}^{2} = 86 - 50 \\ = 36 \\ \bar{x} = 36 \end{array}