Calculate the missing frequency from the following distribution, … - Vidyadip

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

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Answer

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

Median = 24
Hence, median class is 20-30
$\therefore\text{l}=20,\ \text{h}=10,\ \text{f}=\text{a},\ \text{cf}=$ cf of preceding class $=30,\ \frac{\text{N}}{2}=\frac{55+\text{a}}{2}$
Now, median $=\text{l}+\begin{Bmatrix}\text{h}\times\frac{\Big(\frac{\text{N}}{2}-\text{cf}\Big)}{\text{f}}\end{Bmatrix}$
$\Rightarrow24=20+\begin{Bmatrix}10\times\frac{\Big(\frac{55+\text{a}}{2}-30\Big)}{2}\end{Bmatrix}$
$\Rightarrow4=10\times\frac{55+\text{a}-60}{2\text{a}}$
$\Rightarrow4=5\times\frac{\text{a}-5}{\text{a}}$
$\Rightarrow4\text{a}=5\text{a}-25$
$\Rightarrow\text{a}=25$
Thus, yhe missung frequency is 25.

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