Data set P: 3, 7, 7, 11Data set Q: 3, 7, 7, 11, 23The lists give the values in data...

1. INFER what the problem is asking

• We need to compare the means of two data sets
• To compare means, we must calculate both means using the mean formula
• Mean = (sum of all values) ÷ (number of values)

2. SIMPLIFY to find the mean of data set P

• Data set P: 3, 7, 7, 11
• Sum = \(3 + 7 + 7 + 11 = 28\)
• Number of values = 4
• Mean of P = \(28 \div 4 = 7\)

3. SIMPLIFY to find the mean of data set Q

• Data set Q: 3, 7, 7, 11, 23
• Sum = \(3 + 7 + 7 + 11 + 23 = 51\)
• Number of values = 5
• Mean of Q = \(51 \div 5 = 10.2\)

4. INFER the comparison

• Mean of P = 7
• Mean of Q = 10.2
• Since \(7 \lt 10.2\), the mean of data set P is less than the mean of data set Q

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Making arithmetic errors when adding the values or performing division

Students might miscalculate the sums (getting 29 instead of 28 for set P, or 52 instead of 51 for set Q) or make division errors. Even small calculation mistakes lead to wrong mean values, making the comparison incorrect and potentially leading them to select Choice A or Choice C.

Second Most Common Error:

Missing conceptual knowledge: Not remembering that you need to divide by the COUNT of values, not just add them up

Some students might add up the values correctly but forget the division step, or divide by the wrong number (like using the largest value instead of the count). This leads to completely wrong "means" and causes confusion, leading to random guessing among the choices.

The Bottom Line:

This problem tests careful arithmetic execution more than complex reasoning - the concept is straightforward, but precision in calculation is essential for correct comparison.