Question

Question 10
Obtain the mean of the following distribution.

$\begin{array}{cc}\text{Frequency}\left(f_i\right)& \text{Variable}\left(x_i\right)\\ 4& 4\\ 8& 6\\ 14& 8\\ 11& 10\\ 3& 12\end{array}$

Answer 1

We know that,
Mean of the data $\left(\overline{x}\right)=\frac{{\sum }_{i=1}^5{f}_i{x}_i}{{\sum }_{i=1}^5{f}_i}=\frac{f_1{x}_1+f_2{x}_2+f_3{x}_3+f_4{x}_4+f_5{x}_5}{f_1+f_2+f_3+f_4+f_5}$

$=\frac{4\times 4+8\times 6+14\times 8+11\times 10+3\times 12}{4+8+14+11+3}$

$\frac{16+48+112+110+36}{40}=\frac{322}{40}=8.05$

Hence, the mean of the given data is 8.05.