2, 2, 2, 3, 4, 4, 11 What is the median of the seven data values shown?...

1. TRANSLATE the problem information

• Given information:
  • Seven data values: 2, 2, 2, 3, 4, 4, 11
  • Need to find the median
• What this tells us: We need the middle value when data is arranged in order

2. INFER the approach

• Since we have 7 values (odd number), the median will be the single middle value
• The data is already arranged from least to greatest
• For 7 values, the middle position is: \(\frac{7+1}{2} = 4\)

3. Locate the median value

• Count to the 4th position in our ordered list:
  • Position 1: 2
  • Position 2: 2
  • Position 3: 2
  • Position 4: 3 ← This is our median
  • Position 5: 4
  • Position 6: 4
  • Position 7: 11

Answer: B. 3

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about measures of central tendency: Students mix up median with mode (most frequent value) or mean (average).

Since 2 appears three times (most frequently), they might think the median is 2. Or they might calculate the mean: \(\frac{2+2+2+3+4+4+11}{7} = 4\) and select that instead.

This may lead them to select Choice A (2) for mode or Choice C (4) for mean.

Second Most Common Error:

Weak INFER skill: Students miscount positions or don't understand how to find the middle position with 7 values.

They might think the middle is at position 3 or 5, leading to selecting 2 or 4 as the median. Some students count incorrectly and land on the wrong value.

This may lead them to select Choice A (2) or Choice C (4).

The Bottom Line:

Success requires clearly distinguishing median from other statistical measures and accurately counting positions to identify the true middle value in an ordered dataset.