First slide

Introduction to statistics

Question

In a class of 100 students, the average amount of pocket money is Rs.35 per student. If the average is Rs.25 for girls and Rs.50 for boys, then the number
of girls in the class is

Easy

A

20
B

40
C

60
D

80

Solution

Let the number of girls in the class =y
$∴$ Number of boys in the class=100-y
Now, ${\overset{\overset{}{} ¯}{x}}_{1} = 25, n_{1} = y, {\overset{\overset{}{_}}{x}}_{2} = 50, n_{2} = 100 - y$
And, $\begin{aligned} \bar{x} = 35, n_{1} + n_{2} = 100 \\ ∴ 35 = \frac{25 \times y + 50 \times (100 - y)}{100} \end{aligned}$
$\begin{aligned} \Rightarrow 3500 = 25 y + 5000 - 50 y \\ \Rightarrow 25 y = 1500 \Rightarrow y = 60 \\ ∴ Number of girls in the class = 60 \end{aligned}$

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