Team A's average height is 5 ft 11 in and Team B's is 6 ft 2 in. There are 20 players in A and 18 players in B. What is the overall average height (in inches)?
Correct Answer: 72.42 inches
Introduction / Context:When combining groups with different averages and sizes, use weighted averages: convert all measures to a common unit, multiply each group’s average by its headcount, add, then divide by the total headcount.
Given Data / Assumptions:
- Team A: 20 players, average 5 ft 11 in = 71 inches.
- Team B: 18 players, average 6 ft 2 in = 74 inches.
- Find combined average in inches.
Concept / Approach:Overall average = (sum of all individual heights) / (total players). Equivalently, (average_A * count_A + average_B * count_B) / (count_A + count_B).
Step-by-Step Solution:
Convert to inches: 5 ft 11 in = 60 + 11 = 71; 6 ft 2 in = 72 + 2 = 74 Total inches (A) = 71 * 20 = 1420 Total inches (B) = 74 * 18 = 1332 Grand total = 1420 + 1332 = 2752 Total players = 20 + 18 = 38 Combined average = 2752 / 38 ≈ 72.421... ≈ 72.42 inchesVerification / Alternative check:The result must lie between 71 and 74 and lean toward 71–74 weighted by 20 vs 18; 72.42 is consistent and closer to 71 because A has slightly more players.
Why Other Options Are Wrong:
- 72, 70, 70.22 inches: Do not match weighted computation.
- None of these: A precise correct value is available.
Common Pitfalls:Using an unweighted mean of 71 and 74 (which would be 72.5) or mixing feet and inches without converting.
Final Answer:72.42 inches