Question -7

Hint:

Standard Deviation is independent of origin.

For simplicity, let $y_i=(x_i-8)$ ,

so, we have $\displaystyle \sum_{i=1}^{18} y_i=9$ and $\displaystyle \sum_{j=1}^{18} y_j^2=45$ ,

Now,

$\begin{aligned}S^2 & =\frac{1}{18}[\displaystyle \sum_{i=1}^{18} (y_i)^2-\frac{(\displaystyle \sum_{i=1}^{18} y_i)^2}{18}]\\ &= \frac{1}{18}[45 -\frac{(9)^2}{18}]=\frac{81}{36}=\frac{9}{4}\end{aligned}$

$S=\boxed{\frac{3}{2}}$ .

According to question $\sum_{i=1}^{18}x_{i} -144=9$ $\sum_{i=1}^{18}x_{i} = 153$ Also $\sum_{i=1}^{18}x_{i}^{2} -18\sum_{i=1}^{18}x_{i} + 1152 = 45$ $\sum_{i=1}^{18}x_{i}^{2} = 1341$ We know that $SD = \sqrt{\dfrac{\sum_{i=1}^{18}x_{i}^{2} }{18} - \dfrac{(\sum_{i=1}^{18}x_{i})^{2}}{18^{2}}}$ $SD = 1.5$