Find the mean of the following frequency by a suitable method.
C.I. 50-70 70-90 90-110 110-130 130-150 150-170
Frequency 8 12 13 27 18 22

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Solution

Where $h = 20$
C.I frequency
$(f_{i})$ midpoint of C.I
$(x_{i})$ $d_{i} = x_{i} - A$ $d_{i}^{'} = (x_{i} - A) / h$ $f_{i} d_{i}^{'}$
$50 - 70$ $8$ $60$ $60 - 120 = - 60$ $\frac{- 60}{20} = - 3$
$- 24$
$70 - 90$ $12$ $80$ $80 - 120 = - 40$ $\frac{- 40}{20} = - 2$ $- 24$
$90 - 110$ $13$ $100$ $100 - 120 = - 20$ $\frac{- 20}{20} = - 1$ $- 13$
$110 - 130$ $27$ $120$ $120 - 120 = 0$ $0$ $0$
$130 - 150$ $18$ $140$ $140 - 120 = 20$ $\frac{20}{20} = 1$ $18$
$150 - 170$ $22$ $160$ $160 - 120 = 40$ $\frac{40}{20} = 2$ $44$
$\sum f_{i} = 100$ $\sum f_{i} d_{i}^{'} = 1$
By step deviation method mean $(¯ x) = A + \frac{\sum f_{i} d_{i}^{'}}{\sum f_{i}} \times h$

$= 120 + \frac{1}{100} \times 20$

$= 120 + \frac{1}{5}$

$= 120 + 0.2$

mean $= 120.2$

Suggest Corrections

Class interval:	10−30	30−50	50−70	70−90	90−110	110−130
Frequency:	5	8	12	20	3	2

C.I.	50-70	70-90	90-110	110-130	130-150	150-170
Frequency	8	12	13	27	18	22