Find the mean deviation about mean and median for the following data.
$C I$ $5 - 10$ $10 - 15$ $15 - 20$ $20 - 25$ $25 - 30$
$f$ $5$ $12$ $3$ $11$ $9$

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Solution

$C I$ $f_{i}$ $c f$ $M i d - p o i n t$
$x_{i}$ $| x_{i} - M |$ $f_{i} | x_{i} - M |$
$5 - 10$ $5$ $5$ $7.5$ $12.5$ $62.5$
$10 - 15$ $12$ $17$ $12.5$ $7.5$ $90$
$15 - 20$ $3$ $20$ $17.5$ $2.5$ $7.5$
$20 - 25$ $11$ $31$ $22.5$ $2.5$ $27.5$
$25 - 30$ $9$ $40$ $27.5$ $7.5$ $67.5$
$\sum f_{i} = 40$ $\sum f i | x_{i} - M | = 255$
$\Rightarrow$ Here, $\frac{N}{2} = \frac{40}{2} = 20$
$∴$ Median class $= 15 - 20$
$\Rightarrow$ So, $L = 15, c f = 17, f = 3$ and $h = 20 - 15 = 5$
$\Rightarrow$ $M e d i a n (M) = L + \frac{\frac{N}{2} - c f}{f} \times h$
$= 15 + \frac{20 - 17}{3} \times 5$
$= 15 + 5$
$= 20$
$∴$ Median $(M) = 20$
$\Rightarrow$ Mean deviation about the mean $= \frac{\sum f_{i} | x_{i} - M |}{\sum f_{i}}$
$= \frac{255}{40}$
$= 6.37$

Suggest Corrections

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

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

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

$x$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
$f$	$5$	$8$	$15$	$16$	$6$

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

$C I$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$
$f$	$5$	$12$	$3$	$11$	$9$