Calculate the mean deviation for the following data about median.
Class interval $2$ $7$ $12$ $17$ $22$ $27$
Frequency $11$ $12$ $17$ $12$ $20$ $28$

5.12

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2.12

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7.21

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7.54

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Solution

The correct option is D $7.54$
$x_{i}$ $f_{i}$ $f_{i} x_{i}$ $| x_{i} - M e a n |$ $f_{i} | x_{i} - M e a n |$
$2$ $11$ $22$ $15.10$ $166.1$
$7$ $12$ $84$ $10.10$ $121.2$
$12$ $17$ $204$ $5.10$ $86.7$
$17$ $12$ $204$ $0.10$ $1.2$
$22$ $20$ $440$ $4.90$ $98$
$27$ $28$ $756$ $9.90$ $277.2$
$n = \frac{\sum f_{i} x_{i}}{n} = \frac{1710}{100} = 17.10$
Mean about median $= \frac{\sum f_{i} | x_{i} - M e a n |}{n} = \frac{750.4}{100} = 7.54$

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$C I$	$8 - 12$	$13 - 17$	$18 - 22$	$23 - 27$	$28 - 32$	$33 - 37$	$38 - 42$	$43 - 47$
$f$	$14$	$8$	$20$	$7$	$11$	$10$	$24$	$6$

Score $(x)$	$6$	$20$	$8$	$18$	$16$	$12$	$14$	$10$
Frequency $(f)$	$2$	$7$	$11$	$27$	$18$	$13$	$17$	$5$

13, 17, 16, 11, 13, 10, 16, 11, 18, 12, 17

Calculate the mean deviation about the mean for the following frequency distribution :

$\begin{matrix} Class Interval : & 0 - 4 & 4 - 8 & 8 - 12 & 12 - 16 & 16 - 20 Frequency : & 4 & 6 & 8 & 5 & 2 \end{matrix}$

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Class interval	$2$	$7$	$12$	$17$	$22$	$27$
Frequency	$11$	$12$	$17$	$12$	$20$	$28$