AP Statistics Test Scores and Percentile Calculations

Statistical Concepts and Assessments

Test Scores Overview

• A sample of Unit 1 AP Stats Test scores is provided:
  • Scores: 60, 65, 65, 75, 75, 77, 77, 78, 79, 80, 80, 80, 80, 81, 82, 87, 90, 93, 97, 99
  • Mean Score: 80
  • Standard Deviation: 10

Biff's Performance Assessment

• Biff's Score: 65

Percentile Calculation

• To calculate Biff's percentile, identify the number of scores below 65 and calculate his percentile rank using the formula:
  $Percentile Rank = \left(\frac{Number\ of\ scores\ below\ Biff's\ score}{Total\ number\ of\ scores}\right) \times 100$
• In this case:
  • Scores Below 65: 1 (only the score 60 is below 65)
  • Total Scores: 20
• Therefore, we compute:
  $Percentile Rank = \left(\frac{1}{20}\right) \times 100 = 5$
• Conclusion: Biff's percentile is the 5th percentile. This means Biff scored better than 5% of test-takers.

Comparison to Mean

• Mean Score: 80
• Biff's Score: 65
• To find out whether Biff was above or below the mean:
  • Comparison: 65 is less than 80, thus Biff was below the mean.
• To calculate by how many points Biff was below the mean:
  $Points\ Below\ Mean = Mean - Biff's\ Score$
  $Points\ Below\ Mean = 80 - 65 = 15$
• Conclusion: Biff is 15 points below the mean.