Calculate the mean deviation about mean for the data given here:
Class interval $5$ $15$ $25$ $35$ $45$
Frequency $5$ $3$ $9$ $12$ $6$

10.2

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10.4

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10.5

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11.4

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Solution

The correct option is B $10.4$
We have to calculate the mean deviation about the mean for the following data:
$x_{i}$ $f_{i}$ $f_{i} \times x_{i}$ $| x_{i} - Mean |$ $f_{i} \times | x_{i} - Mean |$
$5$ $5$ $25$ $23.14$ $115.7$
$15$ $3$ $45$ $13.14$ $39.42$
$25$ $9$ $225$ $3.14$ $28.26$
$35$ $12$ $420$ $6.86$ $82.32$
$45$ $6$ $270$ $16.86$ $101.16$
$N = \sum f_{i} = 35$
$\sum f_{i} \times x_{i} = 985$
Mean $= ¯ X = \frac{1}{N} (\sum f_{i} x_{i}) = \frac{1}{35} \times (985) = 28.14$
$\sum f_{i} \times | x_{i} - 33.2 | = 366.86$
Mean Deviation $= \frac{1}{N} \times (\sum f_{i} | x_{1} - Mean |) = \frac{366.86}{35} = 10.4$

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Similar questions

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$5$	$3$	$9$	$12$	$6$

Class interval	$0 - 4$	$5 - 9$	$10 - 14$	$15 - 19$	$20 - 24$	$25 - 29$
Frequency	$11$	$12$	$17$	$12$	$20$	$28$

Class	$5$	$15$	$25$	$35$	$45$
Frequency	$5$	$10$	$20$	$5$	$10$

CI	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
$f$	$9$	$13$	$6$	$12$	$9$	$6$	$10$	$15$	$6$	$4$

Calculate mean deviation using median and coefficient of mean deviation :

$\begin{matrix} Class Intervals & 5 - 15 & 15 - 25 & 25 - 35 & 35 - 45 & 45 - 55 F r e q u e n c y & 5 & 4 & 5 & 4 & 2 \end{matrix}$

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