Find the mean of the following distribution by step deviation method.
Class Interval $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$
Frequency $10$ $6$ $8$ $12$ $5$ $9$

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Solution

C.I. Frequency $(f_{i})$ Mid-value(x) $d_{i} = \frac{x - a}{h}$ $f_{i} d_{i}$
$20 - 30$ $10$ $25$ $- 2$ $- 20$
$30 - 40$ $6$ $35$ $- 1$ $- 6$
$40 - 50$ $8$ $45$ $0$ $0$
$50 - 60$ $12$ $55$ $1$ $12$
$60 - 70$ $5$ $65$ $2$ $10$
$70 - 80$ $9$ $75$ $3$ $27$
$\sum f_{i} = 50$ $\sum f_{i} d_{i} = 23$

Here, $a = 45$ and $h = 10$
$∴$ Mean $= a + \frac{\sum f_{i} d_{i}}{\sum f_{i}} \times h$
$= 45 + \frac{23}{50} \times 10$
$= 45 + 4.6 = 49.6$

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Similar questions

\begin{matrix} C l a s s i n t e r v a l & F r e q u e n c y 20 - 30 & 10 30 - 40 & 6 40 - 50 & 8 50 - 60 & 12 60 - 70 & 5 70 - 80 & 9 \end{matrix}

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$5$	$8$	$7$	$12$	$28$	$20$	$10$	$10$

Class	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
frequency	5	8	7	12	28	20	10	10

Class Interval	$0 - 9$	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 50$	$60 - 60$
Frequency	$8$	$10$	$22$	$26$	$18$	$9$	$7$

Marks	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70- 80	80-90	90-100
Frequency	3	5	6	7	8	9	10	12	6	4

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