The median of the distribution given below is 14.4. Find the values of $x$ and $y$, if the total frequency is 20.

Class interval:	0-6	6-12	12-18	18-24	24-30
Frequency:	4	$x$	5	$y$	1

Given:

The median of the distribution given is 14.4. The total frequency is 20.

To do:

We have to find the values of $x$ and $y$.

Solution:

Median $= 14.4$ and $N = 20$

$10 + x + y = 20$

$x+y = 20 - 10 = 10$

$y = 10-x$.....….(i)

Median $= 14.4$ which lies in the class 12-18.

$l = 12, f= 5, F = 4+x$ and $h = 18-12=6$

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

$14.4=12+\frac{\frac{20}{2}-(4+x)}{5}\times 6$

$14.4-12=\frac{10-4-x}{5}\times6$

$2.4(5)=(6-x)6$

$12=36-6x$

$6x=36-12$

$x=\frac{24}{6}=4$

$y = 10 - 4 = 6$            [From (i)]

The values of $x$ and $y$ are $4$ and $6$ respectively. 

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

127 Views

Kickstart Your Career

Get certified by completing the course

Get Started