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.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	5	25	?	18	7

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Answer

Class	Frequency (f)	Cumulative Frequency
0-10	5	5
10-20	25	30
20-30	x	x + 30
30-40	18	x + 48
40-50	7	x + 55

Median is 24 which lies in 20-30
$\therefore$ Median Class = 20-30
Here, $\text{l}=20,\ \frac{\text{n}}{2}=\frac{\text{x}+55}{2},$ c. f of the preceding class $\text{c.f}=30,\ \text{f}=\text{x},\ \text{h}=10$
$\therefore$ Median $\text{l}+\frac{\frac{\text{n}}{2}-\text{c.f}}{\text{f}}\times\text{h}$
$\Rightarrow24=20+\frac{\frac{\text{x}+55}{2}-30}{\text{x}}\times\text{10}$
$\Rightarrow24=20+\frac{\frac{\text{x}+55-60}{2}}{\text{x}}\times10$
$\Rightarrow24=20+\frac{\text{x}-5}{2\text{x}}\times10$
$\Rightarrow24=20+\frac{5\text{x}-25}{\text{x}}$
$\Rightarrow24=\frac{20\text{x}+5\text{x}-25}{\text{x}}$
$\Rightarrow24\text{x}=25\text{x}=25$
$\Rightarrow-\text{x}=-25$
$\Rightarrow\text{x}=25$
Hence, the unknown frequency is 25

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