23, 27, 27, 32, 35, 36, 52What is the range of the 7 scores shown?

1. TRANSLATE the problem information

• Given information:
  • Data set: 23, 27, 27, 32, 35, 36, 52
  • Need to find: range of these 7 scores
• What this tells us: Range means the difference between the largest and smallest values

2. INFER which values to use

• Scan through all the scores to identify:
  • Maximum value: 52 (largest number in the set)
  • Minimum value: 23 (smallest number in the set)
• Strategy: Subtract minimum from maximum

3. SIMPLIFY the calculation

• \(\mathrm{Range = Maximum - Minimum}\)
• \(\mathrm{Range = 52 - 23 = 29}\)

Answer: 29

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about range: Students confuse range with other statistical measures like mean (average) or median (middle value). They might try to add up all the scores and divide by 7, or arrange them in order and pick the middle value.

This leads to confusion and guessing since these approaches don't yield any of the typical answer choices for range problems.

Second Most Common Error:

Weak INFER skills: Students correctly understand that range involves maximum and minimum values, but incorrectly identify these values from the data set. They might miss that 52 is the largest or that 23 is the smallest, especially since the data isn't presented in sorted order.

This may lead to incorrect calculations like \(\mathrm{52 - 27 = 25}\) or \(\mathrm{36 - 23 = 13}\).

The Bottom Line:

Range is one of the simpler statistical measures, but students often overthink it or confuse it with other statistical concepts. The key is recognizing that range always means "biggest minus smallest" - nothing more, nothing less.