$x$ $10$ $20$ $30$ $40$ $50$
$f$ $5$ $7$ $15$ $13$ $10$
From the given distribution, calculate mean deviation about mean.

1.021

No worries! We‘ve got your back. Try BYJU‘S free classes today!

11.231

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10.256

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

12.214

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $10.256$
We have to calculate the mean deviation about the mean for the following data:
$x_{i}$ $f_{i}$ $f_{i} \times x_{i}$ $| x_{i} - M e a n |$ $f_{i} \times | x_{i} - M e a n |$
$10$ $5$ $50$ $23.2$ $116$
$20$ $7$ $140$ $13.2$ $92.4$
$30$ $15$ $450$ $3.2$ $48$
$40$ $13$ $520$ $6.8$ $88.4$
$50$ $10$ $500$ $16.8$ $168$
$N = \sum f_{i} = 50$

$\sum f_{i} \times x_{i} = 1660$

Mean $= ¯ X = \frac{1}{N} (\sum f_{i} x_{i}) = \frac{1}{50} \times (1660) = 33.2$

$\sum f_{i} \times | x_{i} - 33.2 | = 512.8$

Mean Deviation $= \frac{1}{N} \times (\sum f_{i} | x_{1} - M e a n |) = \frac{512.8}{50} = 10.256$

Suggest Corrections

$C . I$	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
$f$	$7$	$10$	$15$	$8$	$10$

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

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

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

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Frequency	$5$	$10$	$20$	$5$	$10$