Question

Three groups of students have average ages 18, 20, and 22 respectively. If the number of students in the three groups is in the ratio 2:3:5, what is the overall average age?

• A. 19.6
• B. 20.6
• C. 15.6
• D. 14.6

Answer 1

Answer:

B. 20.6

Use the weighted average formula.

Average ages:

• Group 1 = 18

• Group 2 = 20

• Group 3 = 22

Number of students ratio:

2:3:5

Overall average:

$\frac{(18 \times 2) + (20 \times 3) + (22 \times 5)}{2+3+5}$

$= \frac{36 + 60 + 110}{10}$

$= \frac{206}{10}$

$= 20.6$

Therefore, the overall average age is:

$\boxed{20.6 \text{ years}}$