Question:A student's scores on the first three of four quizzes are 88, 92, and 83. The student's average score for...

1. TRANSLATE the problem information

• Given information:
  • Three known quiz scores: 88, 92, 83
  • Average of all four quizzes: 89
  • Need to find: The fourth quiz score

2. INFER the solution approach

• Since we know the average and number of quizzes, we can find the total sum needed
• Strategy: Use the average formula to work backwards
• We'll find what the total must be, then subtract what we already have

3. SIMPLIFY to find the required total

• Using \(\mathrm{Average = Sum \div Number\,of\,values}\)
• If average is 89 for 4 quizzes: \(\mathrm{89 = Total\,sum \div 4}\)
• Therefore: \(\mathrm{Total\,sum = 89 \times 4 = 356}\)

4. SIMPLIFY to find the sum of known scores

• Add the first three quiz scores: \(\mathrm{88 + 92 + 83 = 263}\)

5. SIMPLIFY to find the missing score

• Fourth quiz score = Total needed - Sum of first three
• Fourth quiz score = \(\mathrm{356 - 263 = 93}\)

Answer: D. 93

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize they need to work backwards from the average. Instead, they might try to find the average of just the three known scores \(\mathrm{(88 + 92 + 83) \div 3 = 87.67}\), then think the fourth score should be close to this value. This leads to confusion and guessing among the middle-range answer choices.

Second Most Common Error:

Poor SIMPLIFY execution: Students understand the correct approach but make arithmetic errors, particularly when calculating \(\mathrm{89 \times 4 = 356}\) or when adding \(\mathrm{88 + 92 + 83}\). Calculation mistakes at any step cascade through to an incorrect final answer. This may lead them to select Choice A (86) or Choice B (88) depending on where the error occurred.

The Bottom Line:

This problem tests whether students can reverse-engineer from an average to find missing data. The key insight is recognizing that knowing the average and count gives you the total, which then allows you to find the missing piece.