62, 74, 68, 80, 66, 78, 70, 76 What is the median of the data shown? 70 72 74 71...

1. VISUALIZE the problem information

• Given information:
  • Data set: 62, 74, 68, 80, 66, 78, 70, 76
  • Need to find the median
• The data is currently unorganized - we need to sort it to find the middle value(s)

2. INFER the approach

• Since we have 8 numbers (an even count), the median will be the average of the two middle values
• Strategy: Sort the data, identify the 4th and 5th positions, then average those values

3. VISUALIZE by sorting the data

• Arrange in ascending order: 62, 66, 68, 70, 74, 76, 78, 80
• Count to verify: 8 numbers total

4. INFER the middle positions

• With 8 numbers, the middle falls between the 4th and 5th positions
• 4th position: 70
• 5th position: 74

5. SIMPLIFY to find the median

• Median = \(\mathrm{(70 + 74) ÷ 2 = 144 ÷ 2 = 72}\)

Answer: B. 72

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students don't recognize that an even number of data points requires averaging the two middle values. They might just pick one of the middle numbers (either 70 or 74) instead of averaging them.

This may lead them to select Choice A (70) or Choice C (74).

Second Most Common Error:

Poor VISUALIZE execution: Students attempt to find the median without properly sorting the data, trying to identify the "middle" from the original scrambled list.

This leads to confusion and guessing among the answer choices.

The Bottom Line:

The median concept seems straightforward, but students often struggle with the even-count case where averaging is required, or they rush through without properly organizing the data first.