A coach records the ages (in years) of nine participants in a training session as follows: 22, 20, 27, 24,...

1. INFER the approach needed

• Given information: 9 ages that need to be analyzed for their median
• Key insight: Median requires finding the middle value, which means we must order the data first
• With 9 data points, the median will be the 5th value (middle position)

2. Order the data from least to greatest

• Original data: 22, 20, 27, 24, 26, 28, 21, 25, 29
• Ordered data: 20, 21, 22, 24, 25, 26, 27, 28, 29

3. INFER the middle position and identify the median

• Count the positions: 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th
• The 5th position contains the value 25
• Therefore, the median is 25

Answer: C (25)

Why Students Usually Falter on This Problem

Most Common Error Path:

Missing conceptual knowledge of median definition: Students might confuse median with mean and try to add all values and divide by 9.

This approach gives them:

\((22+20+27+24+26+28+21+25+29) \div 9 = 222 \div 9 = 24.67\)

which they might round to either 24 or 25, potentially leading them to select Choice A (24) if they round down.

Second Most Common Error:

Computational error in ordering: Students understand they need to order the data but make mistakes in the ordering process or miscount positions.

For example, if they incorrectly place 24 in the 5th position instead of 25, they would select Choice A (24).

The Bottom Line:

This problem tests whether students truly understand that median requires ordered data and can accurately identify the middle position. While conceptually straightforward, execution errors in ordering or position-counting are the main stumbling blocks.