Find Mean deviation about Mean for the following data
Variate $(x)$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$
Freaquency $(f)$ $15$ $46$ $91$ $162$ $110$ $95$ $82$ $26$ $13$ $2$

3.44

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2.66

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1.47

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7.25

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Solution

The correct option is C $1.47$
$x_{i}$ $f_{i}$ $f_{i} x_{i}$ $| x_{1} - Mean |$ $f_{i} | x_{i} - Mean |$
$0$ $15$ $0$ $3.78$ $56.66$
$1$ $46$ $46$ $2.78$ $127.75$
$2$ $91$ $182$ $1.78$ $161.73$
$3$ $162$ $486$ $0.78$ $125.92$
$4$ $110$ $440$ $0.22$ $24.5$
$5$ $95$ $475$ $1.22$ $116.16$
$6$ $82$ $492$ $2.22$ $182.26$
$7$ $26$ $182$ $3.22$ $83.79$
$8$ $13$ $104$ $4.22$ $54.9$
$9$ $2$ $18$ $5.22$ $10.45$
$n = 642$ $\sum f_{i} x_{i} = 2425$ $\sum f_{i} | x_{i} - Mean | = 944.12$
Mean $= \frac{\sum f_{i} x_{i}}{n} = \frac{2425}{642} = 3.78$
Mean deviation about mean $= \frac{\sum f_{i} | x_{i} - Mean |}{n} = \frac{944.12}{642} = 1.47$

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$x_{i}$	$3$	$5$	$7$	$9$	$11$	$13$
$f_{i}$	$6$	$8$	$15$	$3$	$8$	$4$

Variable( $x$ )	$10$	$15$	$20$	$25$	$30$	$35$	$40$	45
Frequency( $f$ )	$7$	$3$	$8$	$5$	$6$	$8$	$4$	9

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

$C I$	$1 - 5$	$6 - 10$	$11 - 15$	$16 - 20$	$21 - 25$
$f$	$2$	$9$	$5$	$4$	$10$

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Variate $(x)$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$
Freaquency $(f)$	$15$	$46$	$91$	$162$	$110$	$95$	$82$	$26$	$13$	$2$