73, 74, 75, 77, 79, 82, 84, 85, 91 What is the median of the data shown?...

1. INFER what median means for this dataset

• Given information:
  • 9 values: 73, 74, 75, 77, 79, 82, 84, 85, 91
  • Data is already ordered from least to greatest
  • Need to find the median
• Since we have an odd number of values (9), the median is simply the middle value

2. INFER which position is the middle

• With 9 values total, the middle position is the 5th value
• This is because there are 4 values before and 4 values after the 5th position

3. VISUALIZE the position counting

• Count through the ordered values to find the 5th position:
  • 73 (1st), 74 (2nd), 75 (3rd), 77 (4th), 79 (5th), 82 (6th), 84 (7th), 85 (8th), 91 (9th)

Answer: 79

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Students may confuse median with mean, thinking they need to add all values and divide by 9, rather than simply finding the middle value.

This leads to unnecessary calculation and potential confusion, causing them to get stuck or guess randomly.

Second Most Common Error:

Poor VISUALIZE execution: Students miscount positions when identifying the middle value, particularly selecting the 4th value (77) or 6th value (82) instead of the 5th value (79).

This systematic counting error may lead them to select an incorrect answer that seems reasonable since it's close to the actual median.

The Bottom Line:

This problem tests whether students understand that finding the median of an ordered dataset is about position, not calculation. The key insight is recognizing that "median" simply means "middle value" when you have an odd number of data points.