x_i 15 21 27 30 35 f_i 3 5 6 7 8 - NCERT Class XI Mathematics

NCERT Class XI Mathematics - Statistics - Solutions

Question : 8 of 34

Marks: +1, -0

$x_i$	15	21	27	30	35
$f_i$	3	5	6	7	8

Solution:

$x_i$	$f_i$	c.f.	$\left\|x_i-7\right\|$	$f_i\left\|x_i-7\right\|$
15	3	3	15	45
21	5	8	9	18
27	6	14	3	18
30	7	21	0	0
35	8	29	5	40
	29			148

Here,

\frac{N}{2}

\frac{29}{2}

= 14.5

The c.f. just greater than 14.5 is 21 and the corresponding value of x is 30.

So, Median (M) = 30

∴ M.D. about median =

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

\frac{1}{29}

× 148 = 5.1

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