Calculate standard deviation and the coefficient of standard deviation, given the following data:

Income (₹) 5 10 15 20 25 30 35 40

Number of Workers 26 29 40 35 26 18 14 12

Open in App

Solution

Income
(X) No. of workers
(f) fX $x = X - X$ x² fx²

5
10
15
20
25
30
35
40 26
29
40
35
26
18
14
12 130
290
600
700
650
540
490
280 −14.4
−9.4
−4.4
0.6
5.6
10.6
15.6
20.6 207.36
88.36
19.36
0.36
31.36
112.36
243.36
424.36 5391.36
2562.44
774.4
12.6
815.36
2022.48
3407.04
5092.32

∑f = 200 ∑fX = 3880 ∑fx² = 20078

$X = \frac{\sum f X}{\sum f_{}} = \frac{3880}{200} = 19.4 Standard Deviation (σ) = \sqrt{\frac{\sum f x^{2}}{\sum f}} = \sqrt{\frac{20078}{200}} = 10.02 Coefficient of Standard Deviation = \frac{σ}{X} = \frac{10.02}{19.4} = 0.516$

Suggest Corrections

Age (in yrs)	20−25	25−30	30−35	35−40	40−45	45−50	50−55
No. of workers	17	11	8	5	4	3	2

Size	5−10	10−15	15−20	20−25	25−30	30−35	35−40	40−45	45−50
Frequency	6	10	18	30	15	12	10	6	4

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

Variable	5−10	10−15	15−20	20−25	25−30	30−35
Frequency	2	9	29	54	11	5

Class Interval	1−5	6−10	11−15	16−20	21−25	26−30	31−35
Frequency	2	8	15	35	20	10	14

Income (₹)	5	10	15	20	25	30	35	40
Number of Workers	26	29	40	35	26	18	14	12