Calculate mean of the following data:

Values below 10 20 20 40 50

Frequency 20 44 84 120 140

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Solution

Marks Mid Value
(m) f fm

0 − 10
10 − 20
20 − 30
30 − 40
40 − 50 5
15
25
35
45 20
44 − 20 = 24
84 − 44 = 40
120 − 84 = 36
140 − 120 = 20 100
360
1000
1260
900

Σf = 140 Σfm = 3620

For the calculation of mean, first the given less than series is converted in continuous series as above.

$X = \frac{Σ f m}{Σ f} = \frac{3620}{140} = 25.86$
Thus, the mean is 25.86.

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C.I	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	12	?	27	20	17	6

X	Below 10	10−20	20−30	30−40	40−50	50 and Above
Frequency	3	7	15	9	6	4

Class Interval	10−20	20−40	40−70	70−120	120−140
Frequency	4	10	26	8	2

Class Interval	10-20	20-40	40-70	70-120	120-200	Total
Frequency	4	10	26	8	2	50

Variable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	10	20	35	40	25	25	15