4, 10, 18, 4, 4, 5, 6, 5 What is the median of the data set shown?...

1. TRANSLATE the problem requirements

• Given information:
  • Data set: 4, 10, 18, 4, 4, 5, 6, 5
  • Need to find the median

• What this tells us: We need to find the middle value when data is arranged in order

2. VISUALIZE by organizing the data

• Arrange the 8 values in ascending order:
  4, 4, 4, 5, 5, 6, 10, 18

• Count the values: 8 total (even number)

3. INFER the median calculation strategy

• Since we have an even number of values (8), the median is the average of the two middle values
• The middle positions are: 4th and 5th values

4. Identify the middle values

• 4th value: 5
• 5th value: 5

5. Calculate the median

• Median = \((5 + 5) ÷ 2 = 5\)

Answer: B. 5

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students might find the "middle" of the original unordered list rather than understanding they need to arrange the data first.

Looking at the original list (4, 10, 18, 4, 4, 5, 6, 5), they might identify the 4th and 5th values as 4 and 4, leading to a median of 4.

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

Second Most Common Error:

Poor INFER reasoning: Students might not understand that with an even number of data points, they need to average the two middle values. They might just pick one of the middle values arbitrarily.

After correctly ordering the data as 4, 4, 4, 5, 5, 6, 10, 18, they see the middle values are 5 and 5, but instead of averaging them, they just choose 5. While this happens to give the correct answer in this case, it represents flawed understanding that would cause errors in other problems where the two middle values differ.

The Bottom Line:

This problem tests whether students truly understand the complete median procedure: ordering the data AND applying the correct calculation method based on whether there's an even or odd number of values. Many students have partial understanding but miss one crucial step.