Q75 / 160 · TS EAMCET 2019 (03 May Shift 2) · Mathematics

The approximate value of the mean deviation about the mean for the following data is

Class Interval $0 - 2$ $2 - 4$ $4 - 6$ $6 - 8$ $8 - 10$

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

A
$3.56$
B
$4.61$
C
$2.19$
Correct answer
D
$1.78$

Solution

We have,

$y_{i}$	$1$	$3$	$5$	$7$	$9$
$f_{i}$	$1$	$2$	$3$	$2$	$1$

Mean, $\bar{y} = \frac{\sum_{i = 1}^{n} f_{i} y_{i}}{\sum_{i = 1}^{n} f_{i}} = \frac{1 + 6 + 15 + 14 + 9}{1 + 2 + 3 + 2 + 1} = \frac{45}{9} = 5$

Now, mean deviation $= \frac{\sum_{i = 1}^{n} f_{i} |y_{i} - \bar{y}|}{\sum_{i = 1}^{n} f_{i}} = \frac{1 \times 4 + 2 \times 2 + 3 \times 0 + 2 \times 2 + 1 \times 4}{1 + 2 + 3 + 2 + 1} = \frac{16}{9} = 1.78$

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

Class Interval	$0 - 2$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$
Frequency	$1$	$2$	$3$	$2$	$1$

The approximate value of the mean deviation about the mean for the following data is Class Interval 0-2 2-4 4-6 6-8 8-10 Frequency 1 2 3 2 1

Solution

Relevant Questions

The approximate value of the mean deviation about the mean for the following data is

Class Interval $0 - 2$ $2 - 4$ $4 - 6$ $6 - 8$ $8 - 10$

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