Find the mean by direct method of the set of ages in the table below:-

$\begin{matrix} Age (yrs) & 10 & 11 & 12 & 13 & 14 No. of Students in class & 0 & 8 & 3 & 2 & 7 \end{matrix}$

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Solution

$\begin{matrix} X & 10 & 11 & 12 & 13 & 14 & . . . (f) & 0 & 8 & 3 & 2 & 7 & \sum f = 0 + 8 + 3 + 2 + 7 = 20 f.X & 0 & 88 & 36 & 26 & 98 & \sum f . X = 0 + 88 + 36 + 26 + 98 = 248 \end{matrix}$

$¯ ¯¯¯ ¯ X = \frac{\sum f X}{\sum f}$

$¯ ¯¯¯ ¯ X = \frac{248}{20}$

$¯ ¯¯¯ ¯ X = 12.4$

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