Question

Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age (in years)	0−10	10−20	20−30	30−40	40−50
Number of persons	5	25	?	18	7

Answer 1

Let the missing frequency be x.

To find the median let us put the data in the table given below:

Age (in years)	Number of persons (f)	Cumulative frequency (cf)
0−10	5	5
10−20	25	30
20−30	x	30 + x
30−40	18	48 + x
40−50	7	55 + x

The given median is 24,

∴ the median class is 20−30.

∴ l = 20, h = 10, N = 55 + x, f = x and cf = 30

$$\begin{gathered} \mathrm{Median}=l+\left(\frac{{\displaystyle \frac{N}{2}}-cf}{f}\right)\times h \\ \Rightarrow 24=20+\left(\frac{{\displaystyle \frac{55+x}{2}}-30}{x}\right)\times 10 \\ \Rightarrow 24-20=\left(\frac{55+x-60}{2x}\right)\times 10 \\ \Rightarrow 4=\left(\frac{x-5}{2x}\right)\times 10 \\ \Rightarrow 8x=10x-50 \\ \Rightarrow 2x=50 \\ \Rightarrow x=25 \end{gathered}$$

Thus, the missing frequency is 25.