Overview
This lecture explains the concept of percentiles, their meaning in distributions, and introduces related measures such as quartiles and deciles.
Understanding Percentiles
- Percentiles indicate the location of a score within a distribution, ranging from 1st to 99th percentile.
- Scoring at the 59th percentile means you performed better than 59% of the group.
- The nth percentile means a person scored better than n% of people.
- Percentiles divide data into two parts: below and above the percentile point.
- Example: 3rd percentile = 3% below, 97% above; 40th percentile = 40% below, 60% above.
- There are no 0th or 100th percentiles; percentiles go from 1 to 99.
Quartiles and Their Relation to Percentiles
- The 25th percentile is also called Q1 or the first quartile.
- The 50th percentile is Q2, also known as the second quartile or median.
- The 75th percentile is called Q3 or the third quartile.
- Quartiles split the data into four equal parts, each representing 25%.
Deciles and Their Relation to Percentiles
- Deciles divide data into ten equal parts.
- D1 is the first decile and equals the 10th percentile.
- D2 is the second decile and equals the 20th percentile.
- D9 is the ninth decile and equals the 90th percentile.
- Each decile separates the bottom n*10% of scores from the top.
Interpreting Percentiles on Score Reports
- Percentile scores do not reflect the percentage of correct answers but your relative standing.
- A percentile of 65 means you scored better than 65% of your peers, not that you got 65% correct.
- Score reports typically include raw score and percentile columns.
Key Terms & Definitions
- Percentile — The percentage of scores below a particular value in a distribution.
- Quartile — Division of data into four equal parts; Q1 (25th), Q2 (50th/median), Q3 (75th).
- Decile — Division of data into ten equal parts; D1 (10th), D2 (20th), etc.
- Median — The middle value in a distribution, equivalent to the 50th percentile or Q2.
Action Items / Next Steps
- Review examples of calculating and interpreting percentiles.
- Familiarize yourself with quartiles and deciles for upcoming exams.