2, 9, 14, 23, 32 What is the mean of the data shown?...

1. TRANSLATE the question requirement

• The problem asks for the "mean" of the data shown
• Mean = arithmetic average = \(\frac{\mathrm{sum\ of\ all\ values}}{\mathrm{number\ of\ values}}\)
• Data set: 2, 9, 14, 23, 32

2. SIMPLIFY by calculating the sum

• Add all values: \(2 + 9 + 14 + 23 + 32 = 80\)
• Count the values: 5 data points

3. SIMPLIFY to find the final answer

• Mean = \(80 \div 5 = 16\)

Answer: B. 16

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about measures of central tendency: Students confuse mean with median and select the middle value when the data is arranged in order.
When arranged: 2, 9, 14, 23, 32, the middle value is 14.
This may lead them to select Choice A (14).

Second Most Common Error:

Weak SIMPLIFY execution: Students make arithmetic errors when adding the five numbers or when performing the division.
Common calculation mistakes include getting 85 instead of 80 for the sum, leading to \(85 \div 5 = 17\).
This may lead them to select Choice C (17).

The Bottom Line:

This problem tests whether students truly understand what "mean" means versus other statistical measures, and whether they can execute basic arithmetic operations accurately under test conditions.