A fish hatchery has three tanks for holding fish before they are introduced into the wild. Ten fish weighing less...

1. TRANSLATE the problem information

• Given information:
  • Tank A: 10 fish weighing less than 5 ounces
  • Tank B: 11 fish weighing at least 5 ounces but no more than 13 ounces
  • Tank C: 12 fish weighing more than 13 ounces
  • Total: 33 fish
• Need to find: Which value could be the median weight

2. INFER the median position

• For 33 fish, the median is the middle value: position \(\frac{33+1}{2} = 17\)th fish
• When all weights are ordered from least to greatest, we need the 17th value

3. VISUALIZE where each group falls in the ordered list

• Positions 1-10: Tank A fish (all weigh \(\lt\) 5 ounces)
• Positions 11-21: Tank B fish (all weigh 5-13 ounces)
• Positions 22-33: Tank C fish (all weigh \(\gt\) 13 ounces)

4. INFER which tank contains the median

• The 17th fish falls within positions 11-21
• Therefore, the median fish comes from Tank B
• This means the median weight must be between 5 and 13 ounces (inclusive)

5. APPLY CONSTRAINTS to eliminate impossible choices

• Choice A (4.5): Less than 5 ounces → impossible
• Choice B (8): Between 5 and 13 ounces → possible ✓
• Choice C (13.5): Greater than 13 ounces → impossible
• Choice D (15): Greater than 13 ounces → impossible

Answer: B. 8

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand what the median represents or incorrectly calculate its position. They might think the median is simply the average of the three tank groups (around 9-10 ounces) rather than understanding it's the middle value of all 33 individual fish weights.

This conceptual confusion leads to guessing without applying the systematic position-based approach, often selecting Choice C (13.5) because it seems "middle-ish" between the tank ranges.

Second Most Common Error:

Poor INFER reasoning: Students correctly find that the median is the 17th fish but fail to connect this position to the specific tank constraints. They might calculate position 17 correctly but then not realize this constrains the possible values to Tank B's weight range.

This leads them to consider all answer choices as equally valid, often selecting Choice A (4.5) or Choice D (15) without recognizing these violate the position-based constraints.

The Bottom Line:

This problem tests whether students truly understand median as a position-based concept rather than just a "middle number." The key insight is connecting the median's position in the ordered list to the specific constraints that position creates.