ICSE Class X Math 2013 Solved Paper

Question : 3 of 46

Marks: +1, -0

The median of the following observations 11,

12,14,(x-2),(x+4),(x+9),

32,38,47

arranged in ascending order is 24 . Find the value of

x

and hence find the mean.

Solution:

Given :

11,12,14,(x-2),(x+4),(x+9), 32

, 38,47 and median

=24

∵ \;n\;=9 \;\text " (odd) "\;

∴ \;\; \;\text " Median "\;\;=\;{n+1}/{2} \;\text " th term "\;

\;=\;{9+1}/{2} \;\text " th term "\;

\;24\;=5 \;\text " th term "\;

∴ \;\; x+4\;=24

x\;=24-4

x\;=20

Therefore

, 11, 12, 14, (20 - 2), (20 + 4),

(20+9),\;32,38,47

\;=11,12,14,18,24,29,32,38,47

\;\;\text " Now "\; \;\; \;\text " Mean "\;=\;{Σ x}/{n}

=\;\;{11+12+14+18+24+29+32+38+47}/{9}

=\;\;{225}/{9}=25 .

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