First slide

Introduction to statistics

Question

The average salary of male employees in a firm was Rs.520 and that of females was Rs.420. The mean salary of all the employees was Rs.500. The percentage of male employees is

Easy

A

80%
B

60%
C

40%
D

20%

Solution

Since, ${\bar{x}}_{1} = 520, {\bar{x}}_{2} = 420 and \bar{x} = 500$
Also we know $\bar{x} = \frac{n_{1} {\bar{x}}_{1} + n_{2} {\bar{x}}_{2}}{n_{1} + n_{2}}$
$\begin{array}{lrl} \Rightarrow 500 (n_{1} + n_{2}) = 520 n_{1} + 420 n_{2} \\ \Rightarrow 20 n_{1} = 80_{n_{2}} \\ \Rightarrow n_{1} : n_{2} = 4 : 1 \end{array}$
Hence, the percentage of male employees in the firm
$= (\frac{4}{4 + 1}) \times 100 = 80 %$

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