Five Eretmochelys imbricata, a type of sea turtle, each have a nest. The table shows an original data set of...

1. TRANSLATE the problem information

• Given information:
  • Original dataset: 149, 144, 148, 136, 139 eggs (5 nests)
  • New dataset: Same 5 values plus 121 eggs (6 nests total)
  • Need to compare the means of both datasets

2. INFER the most efficient approach

• Key insight: When you add a new data point to a dataset, the mean will:
  • Increase if the new value is greater than the current mean
  • Decrease if the new value is less than the current mean
  • Stay the same if the new value equals the current mean
• Looking at our new value (121) compared to the original data:
  • Smallest original value is 136
  • Since \(121 < 136\), the new value 121 is smaller than ALL original values
  • This means 121 is definitely smaller than the original mean

3. INFER the final comparison

• Since we're adding a value (121) that's smaller than the original mean, the new mean must be smaller than the original mean
• Therefore: \(\mathrm{Original\ mean} > \mathrm{New\ mean}\)

Answer: A. The mean of the original data set is greater than the mean of the new data set.

Alternative Computational Approach:

If you prefer to calculate both means explicitly:

3. SIMPLIFY to find original mean

• Original mean = \((149 + 144 + 148 + 136 + 139) \div 5\)

\(= 716 \div 5\)

\(= 143.2\)

4. SIMPLIFY to find new mean

• New mean = \((149 + 144 + 148 + 136 + 139 + 121) \div 6\)

\(= 837 \div 6\)

\(= 139.5\)

5. Compare:

\(143.2 > 139.5\) ✓

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize the conceptual shortcut that adding a value smaller than all existing values will decrease the mean. Instead, they feel compelled to calculate both means but make arithmetic errors in the process.

Common calculation mistakes include adding incorrectly (getting wrong sums) or dividing incorrectly. For example, getting \(716 \div 5 = 142.2\) instead of 143.2, or \(837 \div 6 = 140.5\) instead of 139.5.

This may lead them to select Choice B or causes confusion leading to guessing.

Second Most Common Error:

Conceptual confusion about means: Students might think that adding any new data point always increases the mean, or they might not understand how the position of the new value relative to existing values affects the mean.

This misconception could lead them to select Choice B (mean increases) or Choice C (means stay equal).

The Bottom Line:

This problem tests whether students understand the conceptual relationship between data values and means, not just their ability to calculate. The most efficient solution requires recognizing patterns rather than computation.