A frequency distribution table for the production of oranges of some farm owners is given below. Find the mean production of oranges by 'assumed mean' method.
Production
(Thousand rupees) 25-30 30-35 35-40 40-45 45-50
No. of farm owners 20 25 15 10 10

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Solution

A frequency distribution table for the production of oranges of some farm owners is given below.

production
(Thousand Rupees) $25 - 30$ $30 - 35$ $35 - 40$ $40 - 45$ $45 - 50$
No. of farm owners $20$ $25$ $15$ $10$ $10$
Now we can prepare a table for calculating mean

Production No. of farm owners $(f_{i})$
Midpoint $x_{i}$ $d_{i} = x_{i} - A$ $f_{i} d_{i}$
$25 - 30$ $20$ $27.5$ $27.5 - 37.5 = - 10$ $- 200$
$30 - 35$ $25$ $32.5$ $32.5 - 37.5 = - 5$
$- 125$
$35 - 40$ $15$ $37.5$ $37.5 - 37.5 = 0$ $0$
$40 - 45$ $10$ $42.5$ $42.5 - 37.5 = + 5$ $50$
$45 - 50$ $10$ $47.5$ $47.5 - 37.5 = + 10$ $100$
$\sum f_{i} = 80$ $\sum f_{i} d_{i} = - 175$

mean $(¯ x) = A + \frac{\sum f_{i} d_{i}}{\sum f_{i}}$

$= 37.5 + \frac{- 174}{80}$

$= 37.5 - \frac{175}{80}$

$= 37.5 - 2.1875$

$= 35.3125$

Suggest Corrections

Expenditure on water (in Rs.)	15-20	20-25	25-30	30-35	35-40	40-45	45-50	50-55	55-60	60-65	65-70
No. of Houses	7	5	7	8	9	11	7	5	4	4	3

Class-interval:	0-10	10-20	20-30	30-40	40-50
No. of workers f:	7	10	15	8	10

Class	0-10	10-20	20-30	30-40	40-50
$f$	6	10	13	7	4

Marks:	30 – 35	35 – 40	40 – 45	45 – 50	50 – 55	55 – 60	60 – 65
Frequency:	14	16	28	23	18	8	3

Money (in Rs.)	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50
No. of students	5	7	5	2	6

Production (Thousand rupees)	25-30	30-35	35-40	40-45	45-50
No. of farm owners	20	25	15	10	10

production (Thousand Rupees)	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
No. of farm owners	$20$	$25$	$15$	$10$	$10$