A teacher recorded the number of hours her students spent on homework last week. The data collected is shown below:2,...

1. TRANSLATE the problem information

• Given information:
  • Raw data: 2, 2, 2, 5, 5, 5, 5, 5, 8, 8, 8, 10, 10
  • Need to find which frequency table correctly represents this data
• What this tells us: We need to count how many times each unique value appears in the dataset

2. VISUALIZE the counting approach

• Strategy: Go through each unique value and count its occurrences
• Organize by identifying unique values first: 2, 5, 8, 10
• Then systematically count each one

3. SIMPLIFY by counting each value's frequency

• Count value 2: 2, 2, 2 → appears 3 times
• Count value 5: 5, 5, 5, 5, 5 → appears 5 times
• Count value 8: 8, 8, 8 → appears 3 times
• Count value 10: 10, 10 → appears 2 times

4. Match results to answer choices

The correct frequency table should show:

• 2 hours: 3 students
• 5 hours: 5 students
• 8 hours: 3 students
• 10 hours: 2 students

This matches choice (A) exactly.

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY skill: Students make counting errors when tallying frequencies

Students might lose track while counting repeated values, especially the five 5's in the dataset. They might count "5, 5, 5, 5" and miss the fifth one, recording frequency as 4 instead of 5. Or they might miscount other values due to careless tallying.

This may lead them to select Choice B which shows incorrect frequencies like 5 appearing only 3 times.

Second Most Common Error:

Poor TRANSLATE reasoning: Students don't fully understand what a frequency table represents

Some students might confuse frequency with the actual data values themselves, or get overwhelmed by answer choices C and D that show obviously incorrect hour values (like 25 hours or 24 hours of homework). This confusion about the basic concept of frequency causes them to make random selections.

This leads to confusion and guessing among the remaining choices.

The Bottom Line:

This problem tests both conceptual understanding of frequency tables and careful execution of counting. Success requires knowing what frequency means AND systematically counting without errors - a combination of concept and precision that trips up many students.