Q. If ${\ \ x}_{1},x_{2},\ldots.,x_{18}$ are observation such that $\ \sum_{j = 1}^{18}{\left( x_{j} - 8 \right) = 9}\ \ \$and$\ \ \ \sum_{j = 1}^{18}{\left( x_{j} - 8 \right)^{2} = 45}$, then these standard derivation of these observations is
A) $\sqrt{\frac{81}{34}}$
B) $5$
C) $\sqrt{5}$
D) $\frac{3}{2}$
Explanation
(d)
Standard deviation
$= {\sqrt{\frac{\sum_{j = 1}^{18}\left( x_{j} - 8 \right)^{2}}{n} - \left( \frac{\sum_{j = 1}^{18}\left( x_{j} - 8 \right)^{\ }}{n} \right)}}^{2}$
$= \sqrt{\frac{45}{18} - \left( \frac{9}{18} \right)^{2}}$
$= \sqrt{\frac{45}{18} - \frac{1}{4} = \sqrt{\frac{81}{36}}}$
$= \frac{9}{6} = \frac{3}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.