A basketball player's points scored in her last 6 games were: 12, 18, 15, 24, 21, 16. What is the...

1. TRANSLATE the problem requirements

• Given information:
  • Basketball scores: 12, 18, 15, 24, 21, 16
  • Need to find the "range"
• What this tells us: Range means the difference between the highest and lowest values in the dataset

2. INFER the systematic approach needed

• To find range, we must first identify two key values:
  • The highest (maximum) score
  • The lowest (minimum) score
• Strategy: Scan through all six scores to find these values

3. Find the highest value

• Looking at: 12, 18, 15, 24, 21, 16
• Highest score: 24

4. Find the lowest value

• Looking at: 12, 18, 15, 24, 21, 16
• Lowest score: 12

5. Calculate the range

• \(\mathrm{Range = Highest\ value - Lowest\ value}\)
• \(\mathrm{Range = 24 - 12 = 12}\)

Answer: C) 12

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion: Many students confuse range with other statistical measures they've learned.

Instead of finding highest minus lowest, they might calculate the mean (average) by adding all scores and dividing by 6, which gives approximately 17.7. Since this doesn't match any answer choice exactly, they become confused and may guess, or they might round to 18 and select Choice E (18).

Second Most Common Error:

Weak INFER skill: Some students understand that range involves highest and lowest values, but fail to systematically scan through the data.

They might quickly glance and incorrectly identify values like 21 as the highest or 15 as the lowest, leading to calculations like \(\mathrm{21 - 15 = 6}\). This leads them to select Choice A (6).

The Bottom Line:

This problem tests whether students truly understand the definition of range versus other statistical concepts, and whether they can systematically process a small dataset to extract the needed information.