The median of the following data is 50. Find the values of $p$ and $q$, if the sum of all the frequencies is 90.

Marks:	20-30	30-40	40-50	50-60	60-70	70-80	80-90
Frequency:	$p$	15	25	20	$q$	8	10

Given:

The median of the given data is 50. The sum of all the frequencies is 90.

To do:

We have to find the values of $p$ and $q$.

Solution:

Median $= 50$ and $N = 90$

$78 + p + q = 90$

$p+q =90 - 78 = 12$

$q = 12-p$.....….(i)

Median $= 50$ which lies in the class 50-60.

$l = 50, f= 20, F = 40+p$ and $h = 60-50=10$

Median $=l+(\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{f}) \times h$

$50=50+\frac{\frac{90}{2}-(40+p)}{20}\times 10$

$50-50=\frac{45-40-p}{2}$

$0(2)=5-p$

$0=5-p$

$p=5$

$q = 12 - 5 = 7$            [From (i)]

The values of $p$ and $q$ are $5$ and $7$ respectively.  

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Updated on: 10-Oct-2022

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