Find out standard deviation and its coefficient of the following series:

Size 10 20 30 40 50 60 70

Frequency 6 8 16 15 33 11 12

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Solution

Size
(X) Frequency
(f) fX Deviation from mean
$(x = X - X)$ Square of deviation x² fx²

10
20
30
40
50
60
70 6
8
16
15
33
11
12 60
160
480
600
1650
660
840 −34.06
−24.06
−14.06
−4.06
5.94
15.94
25.94 1160.08
578.88
197.68
16.48
35.28
254.08
672.88 6960.48
4631.04
3162.88
247.2
1164.24
2794.88
8074.60

Σf = 101 Σfx = 4450 Σfx² = 27035.32

$Mean (X) = \frac{Σ f X}{Σ f} = \frac{4450}{101} = 44.06 Standard deviation (σ) = \sqrt{\frac{Σ f x^{2}}{Σ f}} = \sqrt{\frac{27035.32}{101}} = \sqrt{267.68} = 16.36 Coefficient of S . D . = \frac{σ}{X} = \frac{16.36}{44.06} = 0.37$

Hence, the S.D. is 16.36 and Coefficient of S.D. is 0.37

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Class	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	2	4	6	8	6	4	2

Items	20−30	30−40	40−50	50−60	60−70	70−80	80−90
Frequency	5	10	16	18	12	10	8

Size	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	2	5	7	13	21	16	8	3

Marks	0−10	10−20	20−30	30−40	40−50	50−60	60−70	70−80
Number of Students	5	10	20	40	30	20	10	4

Variables	10	20	30	40	50	60	70
Frequency	6	8	16	15	32	11	12