Question

Obtain the mean of following observations.

Observation Frequency

4 4

8 6

14 8

11 10

3 12

Answer 1

This is a case of mean for an ungrouped frequency distribution .
And in this case mean is
$$\begin{gathered} \overline{x}=\frac{x_1{y}_1+x_2{y}_2+x_3{y}_3+.......x_n{y}_n}{y_1+y_2+y_3+..........y_n} \\ where{x}_1,x_2,......x_{n}arethevaluesofvariablesoccuringwithfrequencies{y}_1,y_2....y_n \end{gathered}$$
So preparing the table for the given question-

$$\begin{gathered} x_i{y}_i{x}_i{y}_i \\ 4416 \\ 8648 \\ 148112 \\ 1110110 \\ 31236 \end{gathered}$$

$\therefore Mean=\frac{(16+48+112+110+36)}{(4+6+8+10+12)}=\frac{322}{40}=8.05$