Question

$10$ is the mean of a set of $7$ observations and $5$ is the mean of a set of $3$ observations. The mean of the combined set is given by

• A. $15$
• B. $10$
• C. $8.5$
• D. $7.5$

Answer 1

The correct option is C $8.5$

We have, $\overline{X_1}=10,\overline{X_2}=5,w_1=7,w_2=3$
$\therefore \overline{X}=\frac{\overline{X_1}{w}_1+\overline{X_1}{w}_1}{w_1+w_2}=\frac{10\times 7+5\times 3}{7+3}=\frac{85}{10}=8.5$