Question

The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is

• A. $\frac{1}{5}$
• B. $\frac{15}{4}$
• C. 4
• D. 8

Answer 1

Answer: (B)

$\frac{15}{4}$

Answer 2

$\frac{x_{1} + x_{2} + ..... + x_{10}}{10} = 4.5$

⇒ $x_{1} + x_{2} + ..... + x_{10} = 45$

and $\frac{x_{11} + x_{12} + ..... + x_{40}}{30} = 3.5$

⇒ $x_{11} + x_{12} + ..... + x_{40} = 105$

∴$x_{1} + x_{2} + ..... + x_{40} = 150$

∴ $\frac{x_{1} + x_{2} + ..... + x_{40}}{40} = \frac{150}{40} = \frac{15}{4}$.