Browse Questions

# The frequency distribution given below find the standard deviation

$\begin{array}{1 1}(A)\;9\\(B)\;5\\(C)\;7\\(D)\;1.38\end{array}$

Toolbox:
• Formula used to solve this problem are :
• Variance $\sigma^2=\large\frac{\sum f_i x_i^2}{\sum f_i} - \bigg(\large\frac{\sum f_ix_i }{\sum f_i } \bigg)^2$
Step 2:
Variance $\sigma^2=\large\frac{\sum f_i x_i^2}{\sum f_i} - \bigg(\large\frac{\sum f_ix_i }{\sum f_i } \bigg)^2$
$\qquad= \sqrt {\large\frac{1393}{60} -\bigg(\large\frac{277}{60} \bigg)^2}$
$\qquad= \sqrt {\large\frac{1393 \times 60 - 277^2}{60 \times 60}}$
$\qquad= \large\frac{1}{60} $$\sqrt {83580-76729} \qquad=\large\frac{1}{60}$$ \sqrt {6851}$
$\qquad= \large\frac{82.77}{60}$
$\qquad= 1.379$
$\qquad= 1.38$
Hence D is the correct answer.