Question

Find f and g if the mean for the data is 54

$$\begin{array}{ccccccc}Class& 0-20& 20-40& 40-60& 60-80& 80-100& Total\\ Frequency& 5& f& g& 13& 9& 50\end{array}$$

Answer 1

Since the total number of observations is given as 50, we know that f+g=23

Let us eliminate one variable by denoting g as 23-f

$$\begin{array}{ccc}ClassMarks& Frequency& f_i{x}_i\\ 10& 5& 50\\ 30& f& 30f\\ 50& 23-f& 1150-50f\\ 70& 13& 910\\ 90& 9& 810\end{array}$$

$\sum f_i$=50 and $\sum f_i{x}_i$=100

54=$\frac{2920-20f}{50}$

20f=220

f = 11

Therefore, g=12.