Calculate mean of the following series by Direct Method:

Mid-value 10 12 14 16 18 20

Frequency 5 8 12 20 10 5

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Solution

Mid Value
(m) Frequency
(f) fm

10
12
14
16
18
20 5
8
12
20
10
5 50
96
168
320
180
100

Σf = 60 Σfm = 914

Calculating the mean by Direct method:

$X = \frac{Σ f m}{Σ f} or, \bar{X} = \frac{914}{60} \Rightarrow \bar{X} = 15.23$

Hence, the mean of the above series is 15.23.

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Class Interval	4−8	8−12	12−16	16−20	20−24	24−28	28−32	32−36	36−40
Frequency	10	12	16	14	10	8	17	5	4

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	7	5	6	12	8	2

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

X	0−10	10−20	20−30	30−60	60−90
Frequency	5	9	20	12	4