71, 72, 73, 76, 77, 79, 83, 87, 93 What is the median of the data shown?...

Step-by-Step Solution

1. TRANSLATE the problem information

• Given information:
  • Data set: 71, 72, 73, 76, 77, 79, 83, 87, 93
  • Need to find the median
• What this tells us: We need the middle value of this ordered list

2. INFER the approach

• Since we have 9 values (odd number), the median will be the middle value
• For 9 values, the middle position is the 5th value when counting from either end
• The data is already arranged in ascending order, so we can proceed directly

3. Locate the median position

• Count to the 5th position: 71 (1st), 72 (2nd), 73 (3rd), 76 (4th), 77 (5th)
• The 5th value is 77

Answer: B. 77

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about measures of central tendency: Students confuse median with mean and calculate the average instead.

They add all values: \(\mathrm{71 + 72 + 73 + 76 + 77 + 79 + 83 + 87 + 93 = 711}\)
Then divide by 9: \(\mathrm{711 ÷ 9 = 79}\)

This leads them to select Choice D (79) instead of the correct median.

Second Most Common Error:

Weak INFER skill: Students don't properly understand which position represents the "middle" for an odd number of values.

They might think the median should be between two values (like in even-numbered sets) or miscalculate the middle position, leading to confusion and potentially selecting Choice A (71) (the minimum) or Choice C (78) (not even in the data set).

The Bottom Line:

Success requires clearly distinguishing median (middle position value) from mean (average value) and correctly identifying what "middle" means for odd-numbered data sets.