Recovering a missing value from partial averages: The average of nine numbers is 50. The average of the first five is 54 and the average of the last three is 52. Find the sixth number.

Introduction / Context:
With the grand average and two block averages known, the single missing term equals the remainder after subtracting the two block totals from the grand total.

Given Data / Assumptions:

• Average of 9 = 50
• Average of first 5 = 54
• Average of last 3 = 52

Concept / Approach:
Translate averages to totals, then compute the sixth term: total9 - total first5 - total last3.

Step-by-Step Solution:

Verification / Alternative check:
Recompose totals to confirm the grand total is maintained.

Why Other Options Are Wrong:

• 34, 44, 30: Do not balance the totals to give a grand average of 50.

Common Pitfalls:
Confusing positions or mistakenly subtracting from the wrong block sum.

Final Answer: