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)

Class	$f_i$	$y_i$	$d_i=y_i-A, A=25$	$f_id_i$	$f_id_i^2$
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

$\sigma^{2}=\frac{\sum\,f_{i} d_{i}^{2}}{\sum\,f_{i}}-\left(\frac{\sum \,f_{i} d_{i}}{\sum \,f_{i}}\right)^{^2}=\frac{900}{10}-\left(-\frac{30}{10}\right)^{^2}$
$\sigma^{2}=90-9=81 \Rightarrow \sigma=9$.