Calculate the mean of the following distribution using step deviation method.
Marks $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$
Number of Students $10$ $9$ $25$ $30$ $16$ $10$

Open in App

Solution

Class
interval
Mid Values
x $_{i}$
Frequency
f $_{i}$
d $_{i}$ =X $_{i}$ -A
u $_{i}$ = $\frac{x_{i} - A}{h}$
f $_{i}$ u $_{i}$
0-10 5 10
-20 -2 -20
10-20 15 9 -10 -1 -9
20-30 25 25 0 0 0
30-40 35 30 10 1 30
40-50 45 16 20 2 32
50-60
55 10 30 3 30
Let $A = 25$ and $h = 10$
$¯ ¯¯¯ ¯ X$ $= A +$ $\frac{h \times \sum f_{i} u_{i}}{\sum f_{i}}$ $= 25 +$ $\frac{10 \times 63}{100}$ $= 25 + 6.3 = 31.3$ .
Hence, the mean is $31.3$ .

Suggest Corrections

Similar questions

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
No. of students	$8$	$15$	$22$	$20$	$10$	$5$

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
No. of students	$5$	$10$	$25$	$30$	$20$	$10$

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
No. of student	$4$	$6$	$10$	$20$	$10$

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	5	10	20	40	30	20	10	4

\begin{matrix} M a r k s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 & 50 - 60 & 60 - 70 & 70 - 80 N o . o f s t u d e n t s & 18 & 16 & 15 & 12 & 10 & 5 & 2 & 2 \end{matrix}

Join BYJU'S Learning Program