Question

Find the mean and standard deviation using short cut method.

$\begin{array}{cccccccccc}{x}_i& 60& 61& 62& 63& 64& 65& 66& 67& 68\\ f_i& 2& 1& 12& 29& 25& 12& 10& 4& 5\end{array}$

Answer 1

$\begin{array}{ccccc}{x}_i& f_i& u=x-64& fu& f{u}^2\\ 60& 2& -4& -8& 32\\ 61& 1& -3& -3& 9\\ 62& 12& -2& -24& 48\\ 63& 29& -1& -29& 29\\ 64& 25& 0& 0& 0\\ 65& 12& 1& 12& 12\\ 66& 10& 2& 20& 40\\ 67& 4& 3& 12& 36\\ 68& 5& 4& 20& 80\\ & 100& & 0& 286\end{array}$

Mean = $\left(\overline{x}\right)=A+\frac{\sum fu}{N}=64+\frac{0}{100}=64$

S.D.=$\left(\sigma \right)=\frac{1}{100}\sqrt{N\sum f{u}^2-(\sum fu{)}^2}$

= $\frac{1}{100}\sqrt{100\times 286-(0{)}^2}$

= $\frac{1}{100}\sqrt{28600}=\frac{1}{100}\times 169.1=1.69$