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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