Question

Calculate mean and standard deviation :

$\begin{array}{cccccc}\text{Class Interval}& 0-10& 10-20& 20-30& 30-40& 40-50\\ \text{Frequency}& 8& 13& 16& 8& 5\end{array}$

Answer 1

$\overline{X}=A+\frac{\sum f{d}^{\prime \prime }}{N}\times i=25+\frac{(-11)}{50}\times 10=25-2.2=22.8$

$S.D.\left(\sigma \right)=\sqrt{\frac{\sum f{d}^{{}^{\prime 2}}}{N}-{\left(\frac{\sum f{d}^{{}^{\prime }}}{N}\right)}^2}\times i=\sqrt{\frac{73}{50}-{\left(\frac{-11}{50}\right)}^2}\times 10$

$=\sqrt{1.46-(0.22{)}^2}\times 10$

$=\sqrt{1.4116}\times 10$

$=1.188\times 10$

$=11.88$