The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed,...

1. TRANSLATE the problem information

• Given information:
  • 8 players had a mean score of 14.5 points
  • After removing the highest score, the remaining 7 players had a mean score of 12 points
  • Need to find the highest score

• What this tells us: We can use the mean formula to find total scores before and after removal

2. INFER the solution approach

• Key insight: The highest score equals the difference between the original total and the remaining total
• Strategy: Calculate both totals using \(\mathrm{Mean = Sum \div Count}\), then find their difference

3. SIMPLIFY to find the total of all 8 scores

• Using \(\mathrm{Sum = Mean \times Count}\):
• Total of 8 scores = \(\mathrm{14.5 \times 8 = 116}\) (use calculator)

4. SIMPLIFY to find the total of the remaining 7 scores

• Total of 7 scores = \(\mathrm{12 \times 7 = 84}\)

5. SIMPLIFY to find the highest score

• Highest score = \(\mathrm{116 - 84 = 32}\)

Answer: C. 32

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER reasoning: Students try to work backwards from the answer choices by testing each one, rather than recognizing the direct relationship between totals.

They might pick an answer choice like 24 and try: "If I remove 24 from a total of 116, I get 92. Then \(\mathrm{92 \div 7 = 13.14...}\)" This approach is unnecessarily complicated and prone to calculation errors.

This leads them to get confused with the arithmetic and may select Choice B (24) or abandon the systematic approach entirely.

Second Most Common Error:

Poor TRANSLATE execution: Students mix up which mean goes with which number of players, calculating something like \(\mathrm{12 \times 8}\) and \(\mathrm{14.5 \times 7}\) instead.

This leads to incorrect totals and completely wrong final answers, causing them to guess among the choices.

The Bottom Line:

This problem rewards students who recognize the elegant relationship between means and totals, rather than trying to verify answer choices through complex backwards reasoning.