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

Age in years	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
No. of persons	$5$	$25$	$?$	$18$	$7$

✓

Answer

Let the frequency of the class $20-30$ be $f_1.$ It is given that median is $35$ which lies
in the class $20-30.$ So $20-30$ is the median class.
Now, lower limit of median class $(l) = 20$
Height of the class $(h) = 10$
Frequency of median class $= (f) = f_1$
Cumulative frequency of preceding median class $(F) = 5 + 25$
Total frequency $(N) =55 + f_1$
Formula to be used to calculate median,
$=\text{l}+\bigg(\frac{\frac{\text{N}}{2}-\text{F}}{\text{f}}\bigg)\text{(h)}$
Where,
$l-$ Lower limit of median class
$h-$ Height of the class
$f-$ Frequency of median class
$F-$ Cumulative frequency of preceding median class
$N-$ Total frequency
Put the values in the above,
$=24=20+\Bigg(\frac{\frac{\text{(55}+\text{f}_1)}{2}-30}{\text{f}_1}\Bigg)(10)$
$\frac{4}{10}=\frac{55+\text{f}_1-60}{2\text{f}_1}$
$2\ \text{f}_1=50$
$\text{f}_1=25$
Hence, the required frequency is $25. $

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