Three groups of students have average ages 18, 20, and 22 respectively. If the number of students in the three groups is in the r…

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?

1. A. 19.6
2. B. 20.6 (Correct answer)
3. C. 15.6
4. D. 14.6

Correct Answer

Option B — 20.6

Detailed Solution & Explanation

The correct answer is 20.6.

Key Points

• The groups are different sizes, so a plain average of 18, 20 and 22 (which is 20) is wrong — the average must be weighted by the ratio 2 : 3 : 5.
• Take the group sizes as 2, 3 and 5 students, totalling 10:
  • Total age = (2 × 18) + (3 × 20) + (5 × 22) = 36 + 60 + 110 = 206
• Overall average = 206 / 10 = 20.6.
• The result sits above the plain average of 20 because the largest group is also the oldest — a useful sanity check on the answer's direction.

Additional Information

• Weighted average = Σ(value × weight) / Σ(weight), and it reduces to the ordinary average only when all weights are equal.
• The result must always lie between the smallest and largest values being averaged — a quick check that discards options 15.6 and 14.6 here on sight.
• The answer is pulled toward the group with the greatest weight, which is why an average of 20.6 sits above the plain mean of 20.

प्रश्न (हिन्दी में)

छात्रों के तीन समूहों की औसत आयु क्रमशः 18, 20 और 22 वर्ष है। यदि तीनों समूहों में छात्रों की संख्या का अनुपात 2 : 3 : 5 है, तो कुल औसत आयु क्या है?

1. A. 19.6
2. B. 20.6
3. C. 15.6
4. D. 14.6