# Determine the mean and standard deviation for the following distribution:

$\begin{array}{1 1}(A)\;4.15,3.049\\(B)\;25,1600\\(C)\;790,87\\(D)\;5.975,2.85\end{array}$

Toolbox:
• The formula to solve this problem:
• Mean $(\bar {x} )=A+\large\frac{\sum f_id_i}{\sum f_i}$
• Standard deviation (SD) $=\sqrt {\large\frac{\sum f_id_i^2}{\sum f_i}- \bigg(\large\frac{\sum f_id_ui}{\sum f_i} \bigg)^2}$
Step 2:
Mean $(\bar {x} )=A+\large\frac{\sum f_id_i}{\sum f_i}$
$\qquad= 9+\large\frac{-121}{40}$
$\qquad= 9- 3.025$
$\qquad= 5.975$
Step 3:
Standard deviation (SD) $=\sqrt {\large\frac{\sum f_id_i^2}{\sum f_i}- \bigg(\large\frac{\sum f_id_ui}{\sum f_i} \bigg)^2}$
$\qquad= \sqrt { \large\frac{691}{40} -\bigg(\large\frac{-121}{40}\bigg)^2}$
$\qquad= \large\frac{1}{40} $$\sqrt {27640 -14641} \qquad=\large\frac{1}{40}$$ \sqrt {12999}$
$\qquad= \large\frac{114.013}{40}$
$\qquad= 2.85$
Hence D is the correct answer.