Question

Find the mean and standard deviation for the following data :

$x_i$	6	10	14	18	24	28	30
$f_i$	2	4	7	12	8	4	3

• A. mean = 6.59, S.D = 19
• B. mean = 8, S.D = 19
• C. mean = 19, S.D = 6.59
• D. mean = 19, S.D = 6

Answer 1

Answer: (C)

Calculation for Mean and Standard Deviation

$x_i$	$f_i$	$f_i{x}_i$	$f_i{x}_i^2$
6	2	12	72
10	4	40	400
14	7	98	1372
18	12	216	3888
24	8	192	4608
28	4	112	3136
30	3	90	2700
130	$\sum f_i=40$	$\sum f_i{x}_i=760$	$\sum f_i{x}_i^2=16176$

Mean $=\frac{\Sigma f_i{x}_i}{\Sigma f_i}=\frac{760}{40}=19$
S.D. $=\sqrt{\frac{\Sigma f_i{x}_i^2}{\Sigma f_i}-{\left(\frac{\Sigma f_i{x}_i}{\Sigma f_i}\right)}^2}$
$=\sqrt{\frac{16176}{40}-{\left(\frac{760}{40}\right)}^2}$
$=\sqrt{404.4-361}=\sqrt{43.4}=\mathrm{6.59.}$
Hence, Mean $=19,\text{ S.D. }=\mathrm{6.59.}$