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UPSC 2013 CDS 2 Math Paper

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Directions (Q. 99–100): two items that follow:

The median of the following distribution is

14.4

and the totalfrequency is

20

:

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

[2013 CDS-II]

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Question : 99 of 100

Marks: +1, -0

What is x equal to?

4
5
6
7

Solution:

Class interval	0 - 6	6 - 12	12 - 18	18 - 24	24 - 30
Frequency	4	$x$	5	$Y$	1
Cumulative frequency	4	$4 + x$	$9 + x$	$x+ y + 9$	$x+ y + 10$

Here

N=x+y+10=20

Median

=14.4

So, the median class is 12-18

Median

=L+\left(\frac{\frac{N}{2}-cf}{f}\right)\times h

\Rightarrow 14.4=12+\left[\frac{\frac{20}{2}-(x+4)}{5}\right]\times 6

\Rightarrow 6-x=2.4\times\frac{5}{6}=2\Rightarrow x=4

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