Question

If the arithmetic mean of the data given below is 28, find the missing frequency.

$\begin{array}{ccccccc}\text{Profit Per}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Retail Shop}& & & & & & \\ \text{Number of}& 12& 18& 27& -& 17& 6\\ \text{Retail Shops}& & & & & & \end{array}$

Answer 1

Let the missing frequency be $f_1$.

Arithmetic Mean = 28

$\begin{array}{cccc}\text{Profit Per}& \text{Number of}& \text{Mid-}& \text{fm}\\ \text{Retail Shop}& \text{Retail}& \text{value}& \\ \text{(in Rs) Class}& \text{Shops (f)}& \left(m\right)& \\ \text{Interval}& & & \\ 0-10& 12& 5& 60\\ 10-20& 18& 15& 270\\ 20-30& 27& 25& 675\\ 30-40& f_1& 35& 35f_1\\ 40-50& 17& 45& 765\\ 50-60& 6& 55& 330\\ & \sum f=80+f_1& & \sum fm\\ & & & =2100+35f_1\end{array}$

$\overline{X}=\frac{\sum fm}{\sum f}$

or $28=\frac{2100+35f_1}{80+f_1}$

or $2240+28f_1=2100+35f_1$

$140=7f_1$

$f_1=20$