Calculate the arithmetic mean of the following frequency distribution by Direct Method:

Class Interval 10−20 20−40 40−70 70−120 120−200

Frequency 4 10 26 8 2

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Solution

Class Interval Mid-Value
(m) Frequency
(f) fm

10 − 20
20 − 40
40 − 70
70 − 120
120 − 200 15
30
55
95
160 4
10
26
8
2 60
300
1430
760
320

∑f = 50 ∑fm = 2870

Using the direct method, arithmetic mean is calculated using the following formula.
$X = \frac{Σ f m}{Σ f} or, X = \frac{2870}{50} = 57.4$
Hence, the arithmetic mean of the series is 57.4

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

Class Interval	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Frequency	5	10	15	20	25	18	7

Class	0-20	20-40	40-60	60-80	80-100	100-120	120-140
Frequency	12	18	15	25	26	15	9

Class Interval	20−25	25−30	30−35	35−40	40−45	45−50	50−55
Frequency	10	12	8	20	11	4	5

Class Interval	10−20	20−40	40−70	70−120	120−200
Frequency	4	10	26	8	2