The following values represent daily temperature changes (in degrees Fahrenheit) recorded over 9 consecutive days: -{4, -1, 0, 3, 6,...

1. TRANSLATE the problem information

• Given information:
  • Original temperature changes: \(\mathrm{-4, -1, 0, 3, 6, 8, 12, 16, 22}\)
  • Each value needs to be increased by 5 degrees
  • Find the median of the new set

• What this tells us: We need to add 5 to every single value, then find the middle value.

2. SIMPLIFY by adding 5 to each value

Transform each temperature change:

• \(\mathrm{-4 + 5 = 1}\)
• \(\mathrm{-1 + 5 = 4}\)
• \(\mathrm{0 + 5 = 5}\)
• \(\mathrm{3 + 5 = 8}\)
• \(\mathrm{6 + 5 = 11}\)
• \(\mathrm{8 + 5 = 13}\)
• \(\mathrm{12 + 5 = 17}\)
• \(\mathrm{16 + 5 = 21}\)
• \(\mathrm{22 + 5 = 27}\)

New data set: \(\mathrm{1, 4, 5, 8, 11, 13, 17, 21, 27}\)

3. INFER the median position

• Since we have 9 values (odd number), the median is the middle value
• For 9 values, the middle position is the 5th position: \(\mathrm{(9 + 1) ÷ 2 = 5}\)th position

4. APPLY CONSTRAINTS to identify the median

Count from the left: \(\mathrm{1}\) (1st), \(\mathrm{4}\) (2nd), \(\mathrm{5}\) (3rd), \(\mathrm{8}\) (4th), \(\mathrm{11}\) (5th)

The 5th value is 11.

Answer: C (11)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students might find the median of the original data set without adding 5 to each value first.

They see the original set \(\mathrm{-4, -1, 0, 3, 6, 8, 12, 16, 22}\) and identify the 5th value as 6, then think the answer should be 6. This may lead them to select Choice A (6).

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly understand they need to add 5 to each value, but make arithmetic errors in the process.

For example, they might miscalculate one or more additions, leading to an incorrect transformed data set. If they get the 5th value wrong due to calculation errors, they might select Choice B (8) or another incorrect option.

The Bottom Line:

This problem tests whether students can systematically apply a transformation to an entire data set before finding a statistical measure. Success requires careful attention to the order of operations: transform first, then find the median.