Data set A: 1, 2, 3, 4, 5, 6, 7 Data set B: 1, 1, 2, 2, 3, 3, 4...

1. TRANSLATE the problem information

• Given information:
  • Data set A: 1, 2, 3, 4, 5, 6, 7
  • Data set B: 1, 1, 2, 2, 3, 3, 4
  • Need to compare the means (arithmetic averages)

• What this tells us: We need to calculate the mean of each data set, then determine which is greater

2. SIMPLIFY to find the mean of data set A

• Mean = (sum of all values) ÷ (number of values)
• Sum: \(1 + 2 + 3 + 4 + 5 + 6 + 7 = 28\)
• Number of values: 7
• Mean of A = \(28 \div 7 = 4\)

3. SIMPLIFY to find the mean of data set B

• Sum: \(1 + 1 + 2 + 2 + 3 + 3 + 4 = 16\)
• Number of values: 7
• Mean of B = \(16 \div 7 \approx 2.29\)

4. Compare the means

• Mean of A = 4
• Mean of B ≈ 2.29
• Since \(4 \gt 2.29\), the mean of data set A is greater than the mean of data set B

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Making arithmetic errors when adding the values in each data set.

Students might miscalculate one or both sums (getting 28 for A or 16 for B), leading to incorrect means. For example, if they miscalculate the sum of data set A as 21, they'd get mean = \(21 \div 7 = 3\), and incorrectly conclude that \(\mathrm{B} \gt \mathrm{A}\). This may lead them to select Choice C (mean of \(\mathrm{A} \lt \mathrm{B}\)).

Second Most Common Error:

Conceptual confusion about mean calculation: Forgetting to divide by the number of values, or dividing by the wrong number.

Some students might correctly find the sums (28 and 16) but then divide by the number of unique values instead of total values, or make other division errors. This could lead to various incorrect means and wrong answer selection or cause confusion and guessing.

The Bottom Line:

This problem tests fundamental understanding of mean calculation and careful arithmetic. Success requires both knowing the mean formula and executing the calculations accurately for both data sets.