Data set X: 5, 9, 9, 13Data set Y: 5, 9, 9, 13, 27The lists give the values in data...

1. TRANSLATE the problem requirements

• Given information:
  • Data set X: 5, 9, 9, 13
  • Data set Y: 5, 9, 9, 13, 27
• What we need: Compare the means of the two data sets

2. TRANSLATE what "mean" means mathematically

• Mean = (sum of all values) ÷ (number of values)
• We need to calculate the mean for each data set, then compare the results

3. SIMPLIFY by calculating the mean of data set X

• Sum of X values: \(\mathrm{5 + 9 + 9 + 13 = 36}\)
• Number of values in X: 4
• Mean of X = \(\mathrm{36 \div 4 = 9}\)

4. SIMPLIFY by calculating the mean of data set Y

• Sum of Y values: \(\mathrm{5 + 9 + 9 + 13 + 27 = 63}\)
• Number of values in Y: 5
• Mean of Y = \(\mathrm{63 \div 5 = 12.6}\)

5. Compare the means

• Mean of X = 9
• Mean of Y = 12.6
• Since \(\mathrm{9 \lt 12.6}\), the mean of data set X is less than the mean of data set Y

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may confuse "mean" with other measures like median or mode, especially if they see repeated values (like the two 9's in both data sets).

They might think the repeated 9's somehow represent the "typical" value and conclude the means are the same, leading them to select Choice C.

Second Most Common Error:

Poor SIMPLIFY execution: Students make arithmetic errors when adding the values or dividing. For example, incorrectly calculating \(\mathrm{63 \div 5}\) as 13 instead of 12.6, or miscounting the number of values in each data set.

This leads to incorrect mean calculations and wrong comparisons, potentially causing them to select Choice A or get confused and guess.

The Bottom Line:

This problem tests whether students truly understand what "mean" represents and can execute the calculation accurately. The presence of identical starting values in both data sets can create a false impression that the means should be equal, when the key insight is recognizing how the additional value (27) affects the overall average.