Q75 / 160 · TS EAMCET 2020 (09 Sep Shift 1) · Mathematics

The mean deviation about the mean for the following data is

Class Interval $0 - 4$ $4 - 8$ $8 - 12$ $12 - 16$

Frequency $4$ $3$ $2$ $1$

A
$6$
B
$3.6$
Correct answer
C
$3.2$
D
$10$

Solution

$f_{i}$	$f_{i}$	$x_{i}$	$f_{i} x_{i}$	$\|x_{i} - x\|$	$f_{i} \|x_{i} - x\|$
4	0-4	2	8	4	16
3	4-8	6	18	0	0
2	8-12	10	20	4	8
1	12-16	14	14	8	8
10			60		32

$x = \frac{\sum f_{i} x_{i}}{N} = \frac{60}{10} = 6$

$M . D .$ $= \frac{\sum_{i = 1}^{4} f_{i} |x_{i} - x|}{N} = \frac{32}{10} = 3.2$

Hence, the correct answer is option: 'C'.

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