Q. Mean and standard deviation from the following observations of marks of 5 students of a tutorial group (marks out of 25)8, 12, 13, 15, 22 are respectively
A) 14, 4.604
B) 15, 4.604
C) 14, 5.604
D) None of these
Explanation
(a)
$\overline{x} = \frac{8 + 12 + 13 + 15 + 22}{5} = \frac{70}{5} = 14$
$\sigma = \sqrt{\frac{\begin{array}{r}
(8 - 14)^{2} + (12 - 14)^{2} + (13 - 14)^{2} \\
+ (15 - 14)^{2} + (22 - 14)^{2}
\end{array}}{5}}$
$= \sqrt{\frac{36 + 4 + 1 + 1 + 64}{5}}$
$= \sqrt{212} = 4.604$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.