Calculate the arithmetic mean, standard deviation and variance from the following distribution:

Class : 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

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Solution

Size Mid Value
(m) (f) fm Deviation from mean
x x² fx²

0 − 5
5 − 10
10 − 15
15 − 20
20 − 25
25 − 30
30 − 35
35 − 40 2.5
7.5
12.5
17.5
22.5
27.5
32.5
37.5 2
5
7
13
21
16
8
3 5
37.5
87.5
227.5
472.5
440
260
112.5 19.4
14.4
9.4
4.4
.6
5.6
10.6
15.6 376.36
207.36
88.36
19.36
.36
31.36
112.36
243.36 752.72
1036.8
618.52
251.68
7.56
501.76
898.88
730.08

Σf = 75 Σfm = 1642.5 Σfx² = 4798

$X = \frac{Σ f m}{Σ f} = \frac{1642.5}{75} = 21.9 S D = \sqrt{\frac{Σ f x^{2}}{Σ f}} = \sqrt{\frac{4798}{75}} = \sqrt{63.97} = 7.99 Variance (σ^{2}) = \frac{Σ f x^{2}}{Σ f} = \frac{4798}{75} = 63.97$

Suggest Corrections

Class-interval:	10−15	15−20	20−25	25−30	30−35	35−40
Frequency:	30	35	75	40	30	15

Class:	1–10	10–20	20–30	30–40	40–50	50–60
Frequency:	11	29	18	4	5	3

Classes	0-10	10-20	20-30	30-40	40-50
Frequency	5	8	15	16	6

Class	:	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