Question

What is the standard deviation of the following series

Measurements	0-10	10-20	20-30	30-40
Frequency	1	3	4	2

• A. 81
• B. 7.6
• C. 9
• D. 2.26

Answer 1

Answer: (C)

9

Answer 2

Class	fi	yi	d = yi − A, A = 25	fidi	fidi2
0-10	1	5	– 20	– 20	400
10-20	3	15	– 10	– 30	300
20-30	4	25	0	0	0
30-40	2	35	10	20	200
Total	10			– 30	900

$\sigma^{2} = \frac{\sum f_{i}d_{i}^{2}}{\sum f_{i}} - \left( \frac{\sum f_{i}d_{i}}{\sum f_{i}} \right)^{2} = \frac{900}{10} - \left( \frac{- 30}{10} \right)^{2}$

$\sigma^{2} = 90 - 9 = 81$⇒ σ = 9.