Data set A: 2, 5, 5, 8, 10, 20 Data set B: 5, 5, 8, 10, 20 The lists give...

1. TRANSLATE the problem requirements

• Given information:
  • Data set A: 2, 5, 5, 8, 10, 20
  • Data set B: 5, 5, 8, 10, 20
  • Need to compare the means of both data sets

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

2. SIMPLIFY by calculating the mean of Data set A

• Add all values: \(2 + 5 + 5 + 8 + 10 + 20 = 50\)
• Count the values: 6 numbers total
• Mean = Sum ÷ Count = \(50 \div 6 \approx 8.33\)

3. SIMPLIFY by calculating the mean of Data set B

• Add all values: \(5 + 5 + 8 + 10 + 20 = 48\)
• Count the values: 5 numbers total
• Mean = Sum ÷ Count = \(48 \div 5 = 9.6\)

4. Compare the results

• Mean of A ≈ 8.33
• Mean of B = 9.6
• Since \(8.33 \lt 9.6\), the mean of data set A is less than the mean of data set B

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Arithmetic errors when adding the data values or dividing by the count

Students might miscalculate the sums (getting 51 instead of 50 for set A, or 47 instead of 48 for set B) or make division errors. For example, if they calculate \(51 \div 6 = 8.5\) and \(47 \div 5 = 9.4\), they might still get the right comparison, but if they get \(49 \div 6 \approx 8.17\) and \(48 \div 5 = 9.6\), the comparison remains correct. However, more significant errors like getting means of 8.5 and 8.8 could lead them to select Choice A (mean of A is greater than mean of B).

Second Most Common Error:

Missing conceptual knowledge: Not understanding what "mean" means or confusing it with other statistics like median or mode

Students who don't know that mean equals sum divided by count might try to find the middle values (median) or most frequent values (mode). This leads to confusion since both data sets have the same mode (5 appears twice in each), and they might incorrectly conclude the means are equal, leading them to select Choice C.

The Bottom Line:

This problem tests whether students can accurately execute the mean calculation formula and handle basic arithmetic under pressure. The conceptual understanding of mean is straightforward, but computational accuracy determines success.