Question

Calculate the mean of the following distribution:
$\begin{array}{cc}ClassInterval& Frequency\\ 0-10& 8\\ 10-20& 5\\ 20-30& 12\\ 30-40& 35\\ 40-50& 24\\ 50-60& 16\end{array}$

Answer 1

$\begin{array}{ccccc}Class& Frequency& Class& u_i=\frac{x_i-A}{h}& f_i{u}_i\\ Interval& \left(f_i\right)& mark& & \\ & & x_i& & \\ 0-10& 8& 5& -3& -24\\ 10-20& 5& 15& -2& -10\\ 20-30& 12& 25& -1& -12\\ 30-40& 35& A\left(35\right)& 0& 0\\ 40-50& 24& 45& 1& 24\\ 50-60& 16& 55& 2& 32\\ & \sum f_i=100& & & \sum f_i{u}_i=10\end{array}$

From the table, A = 35 and h = 10

Mean $\left(\overline{x}\right)=A+(\frac{\sum f_i{u}_i}{\sum f_i}\times h)$
$=35+(\frac{10}{100}\times 10)=35+1=36$