Question:The scores on a quiz are listed below.2, 2, 2, 2, 5, 5, 5, 9, 9Which frequency table correctly represents...

1. TRANSLATE the problem information

• Given information:
  • Raw data: 2, 2, 2, 2, 5, 5, 5, 9, 9 (9 total scores)
  • Bin ranges: 1-3, 4-6, 7-9
  • Need to find: How many scores fall into each bin

• What this tells us: We need to sort and count our data values according to which bin range they belong to.

2. INFER the approach

• Strategy: For each bin range, count how many of our data values fall within that range
• Work through each bin systematically to avoid missing any values

3. SIMPLIFY by counting values in each bin

For bin 1-3 (includes values 1, 2, and 3):

• Looking at our data: 2, 2, 2, 2, 5, 5, 5, 9, 9
• The 2's belong here: four 2's
• Frequency = 4

For bin 4-6 (includes values 4, 5, and 6):

• Looking at our data: 2, 2, 2, 2, 5, 5, 5, 9, 9
• The 5's belong here: three 5's
• Frequency = 3

For bin 7-9 (includes values 7, 8, and 9):

• Looking at our data: 2, 2, 2, 2, 5, 5, 5, 9, 9
• The 9's belong here: two 9's
• Frequency = 2

4. Verify your work

• Check: \(4 + 3 + 2 = 9\) ✓ (matches total number of scores)

Answer: A

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misunderstand what belongs in the "Bin" column versus the "Frequency" column, or don't understand that bins represent ranges of values.

They might think the individual data values (2, 5, 9) should be listed as separate bins, or confuse the data values with the frequencies. This conceptual confusion about frequency table structure leads them to select Choice B or get stuck and guess randomly.

Second Most Common Error:

Poor SIMPLIFY execution: Students make counting errors or misplace values into wrong bins (like putting 5's in the 1-3 bin instead of 4-6 bin).

Careless counting or misunderstanding which values belong to which ranges can lead to incorrect frequency counts, potentially causing them to select Choice C or abandon systematic solution and guess.

The Bottom Line:

This problem tests whether students truly understand the fundamental structure of frequency tables - that bins represent ranges of possible values, and frequencies represent how many actual data points fall into each range. The key insight is organizing the counting process systematically rather than trying to handle all the data at once.