13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, ...

NCERT Class XI Mathematics - Statistics - Solutions

Question : 3 of 34

Marks: +1, -0

13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Solution:

Arranging the data in ascending order,

we have

10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18

Here n = 12 (which is even)

So median is the average of 6th and 7th observations

∴ Median (M) =

\frac{13+14}{2}

\frac{27}{2}

= 13.5

$x_i$	10	11	11	12	13	13	14	16	16	17	17	18	Total
$\left\| x_i - 13.5 \right\|$	3.5	2.5	2.5	1.5	0.5	0.5	0.5	2.5	2.5	3.5	3.5	4.5	28

∴ M.D. about median =

\frac{1}{n} \sum\limits_{i=1}^{n} \left| x_i - M \right|

\frac{1}{12}

× 28 = 2.33

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