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	Frequency	yi	$u_{i} = \frac{y_{i} - A}{10}$, A = 25	fiui	fiui2
0-10	1	5	– 2	– 2	4
10-20	3	15	– 1	– 3	3
20-30	4	25	0	0	0
30-40	2	35	1	2	2
	10			– 3	9

$\sigma^{2} = c^{2}\left\lbrack \frac{\sum f_{i}u_{i}^{2}}{\sum f_{i}} - \left( \frac{\sum f_{i}u_{i}^{2}}{\sum f_{i}} \right)^{2} \right\rbrack = 10^{2}\left\lbrack \frac{9}{10} - \left( \frac{- 3}{10} \right)^{2} \right\rbrack = 90 - 9 = 81$ ⇒ σ = 9