If the median of 60 observations, given below is 28.5 find the values of x and y.

Class Interval(CI)	Frequency(f)
0-10	5
10-20	x
20-30	20
30-40	15
40-50	y
50-60	5

Given: Median = 28.5 and number of observations = 60.

To find: Here we have to find the values of x and y. 

Solution:

Cumulative frequency (CF) table for the following data is as below:

Here,

Number of observations (n) = 60

So,

$\frac{n}{2}$ ​= 30

Since, median is 28.5, median class is 20−30

Hence, l = 20, h = 10, f = 20, cf = 5 + x.

Therefore,

Median = $l+\left(\frac{\frac{n}{2} \ -\ cf}{f}\right) h$

$28.5$ = $20\ +$ $\left(\frac{30\ \ -\ \ 5\ \ -\ \ x}{20}\right)$ $\times \ 10$

$28.5$ = $20\ +$ $\left(\frac{25\ \ -\ \ x}{2}\right)$

$28.5\ -\ 20$ = $\left(\frac{25\ \ -\ \ x}{2}\right)$

$8.5\times2$ = $25\ −\ x$

$x$ = 8  

Also,

$45\ +\ x\ +\ y$ = $60$  

$y$ = $60\ −\ 45\ −\ x$

$y$ = $15\ −\ 8$

$y$ = $7$

Hence, $x$ = 8, $y$ = 7.

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Updated on: 10-Oct-2022

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