Question

The S.D. of the following data is nearly

$x_i$	140	145	150	155	160	165	170	175
$f_i$	4	6	15	30	36	24	8	2

• A. 8.64
• B. 7.26
• C. 7.05
• D. None

Answer 1

Answer: (B)

Let us assume an arbitary mean a = 155.
Following table is constructed :

$X_i$	$f_i$	$u_i-\frac{X_i-155}{5}$	$u_i^2$	$f_i{u}_i$	$f_i{u}_i^2$
140	4	-3	9	-12	36
145	6	-2	4	-12	24
150	15	-1	1	-15	15
155	30	0	0	0	0
160	36	1	1	36	36
165	24	2	4	48	96
170	8	3	9	24	72
175	2	4	16	8	32
Total	125			77	311

$\therefore$ Variance = $={\sigma }^2=c^2\left(\frac{\sum f_i{u}_i^2}{n}-{\left(\frac{\sum f_i{u}_i}{n}\right)}^2\right)$
$=25\times \left(\frac{311}{125}-{\left(\frac{77}{125}\right)}^2\right)$
$=25\times \frac{311}{125}-\frac{25\times 77\times 77}{125\times 125}$
$=62.2-9.4864=52.7136$
$\Rightarrow S.D=\sqrt{52.7136}=7.26$ nearly