Question

A group of $10$ items has arithmetic mean $6$. If the arithmetic mean of $4$ of these items is $7.5$, then the mean of the remaining items is

• A. $6.5$
• B. $5.5$
• C. $4.5$
• D. $5.0$

Answer 1

The correct option is D $5.0$

We have, $\overline{X}=6,\overline{X_1}=7.5,\overline{X_2}=?,w_1=4,w_2=6$
$\therefore \overline{X}=\frac{\overline{X_1}{w}_1+\overline{X_2}{w}_1}{w_1+w_2}=\frac{7.5\times 4+\overline{X_2}\times 6}{10}=6\Rightarrow \overline{X_2}=5$