First slide

Introduction to statistics

Question

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

Moderate

A

80
B

60
C

40
D

20

Solution

Let $n_{1}$ and $n_{2}$ be the number of boys and girls respectively in the class.
We have $\bar{X_{1}} = 52, \bar{X_{2}} = 42$ and $\bar{X} = 50$
$\begin{array}{l} ∴ \bar{X} = \frac{n_{1} \bar{X_{1}} + n_{2} \bar{X_{2}}}{n_{1} + n_{2}} \\ \Rightarrow 50 = \frac{52 n_{1} + 42 n_{2}}{n_{1} + n_{2}} \Rightarrow 8 n_{2} = 2 n_{1} \Rightarrow n_{1} = 4 n_{2} \end{array}$
$∴$ Percentage of boys $= \frac{n_{1}}{n_{1} + n_{2}} \times 100 = \frac{4 n_{2}}{5 n_{2}} \times 100 = 80$

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