Data set X: 10, 15, 20, 25 Data set Y: 5, 10, 15, 20, 25 The lists give the values...

1. TRANSLATE the problem requirements

• Given information:
  • Data set X: 10, 15, 20, 25
  • Data set Y: 5, 10, 15, 20, 25
  • Need to compare the means of both data sets

2. SIMPLIFY to find the mean of data set X

• Add all values: \(10 + 15 + 20 + 25 = 70\)
• Count the values: 4 numbers
• Calculate mean: \(70 \div 4 = 17.5\)

3. SIMPLIFY to find the mean of data set Y

• Add all values: \(5 + 10 + 15 + 20 + 25 = 75\)
• Count the values: 5 numbers
• Calculate mean: \(75 \div 5 = 15\)

4. INFER the comparison result

• Compare the means: \(17.5\) vs \(15\)
• Since \(17.5 \gt 15\), the mean of data set X is greater than the mean of data set Y

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Poor SIMPLIFY execution: Making arithmetic errors when adding the values or counting incorrectly

Students might miscalculate one of the sums (getting \(65\) instead of \(70\) for set X, or \(70\) instead of \(75\) for set Y), or miscount the number of values in each set. For example, if they get mean of X = \(16.25\) and mean of Y = \(15\), they might still select Choice A, but if they get mean of X = \(16.25\) and mean of Y = \(17.5\) due to calculation errors, this leads them to select Choice B.

Second Most Common Error:

Weak TRANSLATE reasoning: Misunderstanding what "compare the means" requires

Some students calculate only one mean correctly but make errors with the other, or they might calculate both means but then compare them incorrectly (confusing which is greater). This leads to confusion and potentially selecting the wrong comparison statement.

The Bottom Line:

This problem tests careful arithmetic execution more than complex reasoning - small computational errors can completely flip the correct answer choice.