The weights, in pounds, for 15 horses in a stable were reported, and the mean, median, range, and standard deviation...

1. TRANSLATE the problem information

• Given information:
  • 15 horses with reported weights
  • Mean, median, range, and standard deviation were calculated
  • The lowest-weight horse actually weighs 10 pounds less than reported
  • Need to find which statistic remains unchanged after correction

2. INFER the approach

The key insight is that we're decreasing only the lowest value, so we need to think about how each statistic responds to this specific change. Since the lowest value was already the smallest, decreasing it further keeps it in the same relative position but changes its actual value.

3. CONSIDER ALL CASES by examining each statistic

Mean Analysis:

• Mean = (sum of all weights) ÷ 15
• Decreasing one weight by 10 pounds decreases the sum by 10 pounds
• New mean = (original sum - 10) ÷ 15 = original mean - \(\frac{10}{15}\) ≈ original mean - 0.67
• Mean changes

Median Analysis:

• Median = 8th value when all 15 weights are ordered from least to greatest
• The corrected horse was already the lowest, so it stays in position #1
• The horse in position #8 (median position) is completely unaffected
• Median stays the same

Range Analysis:

• Range = highest weight - lowest weight
• Decreasing the lowest weight by 10 pounds increases the difference
• New range = highest weight - (lowest weight - 10) = original range + 10
• Range changes

Standard Deviation Analysis:

• INFER that standard deviation measures how far data points spread from the mean
• Since the mean decreased (from step above), and one data point moved even further from this new mean, the overall spread changes
• Standard deviation changes

4. APPLY CONSTRAINTS to select the answer

Only the median remains unchanged because it depends on positional order, not the specific values at the extremes.

Answer: B. Median

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students incorrectly think that changing any data value affects the median. They reason "if we change a weight, then the median must change too" without understanding that median depends on the middle position, not on extreme values.

This may lead them to select Choice A (Mean) because they incorrectly eliminate median as a possibility and guess among the remaining options.

Second Most Common Error:

Inadequate CONSIDER ALL CASES execution: Students correctly identify that the median doesn't change but fail to systematically verify that the other three statistics do change. They might think range stays the same because "we're just correcting an error, not adding a new horse."

This leads to confusion and guessing among multiple choices.

The Bottom Line:

This problem tests whether students truly understand what each statistic measures and how they respond to data changes. The key insight is recognizing that median depends on position (ordinal), while the other three statistics depend on actual values (cardinal).