The table above shows the number of students from two different high schools who completed summer internships in each of...

1. TRANSLATE the data from the table

• Extract the correct data sets:
  • Foothill High School: 87, 80, 75, 76, 70
  • Valley High School: 44, 54, 65, 76, 82

2. SIMPLIFY to find the means

• Foothill mean = \((87 + 80 + 75 + 76 + 70) ÷ 5 = 388 ÷ 5 = 77.6\)
• Valley mean = \((44 + 54 + 65 + 76 + 82) ÷ 5 = 321 ÷ 5 = 64.2\)

3. VISUALIZE by ordering data to find medians

• Foothill ordered: 70, 75, 76, 80, 87
  • With 5 values, the median is the 3rd value = 76
• Valley ordered: 44, 54, 65, 76, 82
  • With 5 values, the median is the 3rd value = 65

4. INFER which statements are true

• Statement I: Is Foothill mean > Valley mean?
  • \(77.6 \gt 64.2\) ✓ TRUE
• Statement II: Is Foothill median > Valley median?
  • \(76 \gt 65\) ✓ TRUE

Answer: C (Both I and II are true)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may misread the table and accidentally use the wrong row of data for one of the schools, or confuse which numbers belong to which year.

For example, a student might accidentally use Valley's data when calculating Foothill's statistics. This would lead to comparing Valley to itself, or getting completely incorrect values, causing confusion and random guessing.

Second Most Common Error:

Inadequate SIMPLIFY execution: Students make arithmetic errors when calculating means, particularly when adding the five numbers or performing the division.

A common mistake is getting the sum wrong (like getting 378 instead of 388 for Foothill), leading to mean = 75.6 instead of 77.6. This could make them incorrectly conclude that Statement I is false, leading them to select Choice B (II only).

The Bottom Line:

This problem tests careful data extraction and systematic calculation of basic statistical measures. Success depends on methodical organization and accurate arithmetic rather than complex mathematical reasoning.