Question

Find the mean of the following data:
\[ \begin{array}{c|c|c|c|c|c} \text{Variable} & 4 & 6 & 8 & 10 & 12 \\ \hline \text{Frequency} & 4 & 8 & 14 & 11 & 3 \end{array} \]

Hint:

Multiply each value by its frequency, sum them, then divide by total frequency.

Answer 1

Mean is given by:
\[ \bar{x} = \frac{\sum f_i x_i}{\sum f_i}. \] \[ \sum f_i x_i = (4 \times 4) + (6 \times 8) + (8 \times 14) + (10 \times 11) + (12 \times 3). \] \[ = 16 + 48 + 112 + 110 + 36 = 322. \] \[ \sum f_i = 4 + 8 + 14 + 11 + 3 = 40. \] \[ \bar{x} = \frac{322}{40} = 8.05. \]