Overview
This lesson explains quartiles and percentiles, how to interpret them on data sets, and how to calculate the number of data values based on a given percentile.
Quartiles and Percentiles Basics
- Percentiles indicate the value below which a given percent of data values fall.
- Quartile 1 (Q1) is the 25th percentile, meaning 25% of data values are at or below Q1.
- 75% of data values are at or above the 25th percentile (Q1).
- The median or Quartile 2 (Q2) is the 50th percentile, meaning half of the values are at or below it.
- The other half (50%) are at or above the 50th percentile (median).
- Quartile 3 (Q3) is the 75th percentile, meaning 75% of data are at or below Q3.
- 25% of data values are at or above the 75th percentile (Q3).
Interpreting Percentiles in Data Sets
- The 28th percentile means 28% of values are at or below it, and 72% are at or above.
- The 70th percentile means 70% of values are at or below it, and 30% are at or above.
Calculating Number of Values at Certain Percentiles
- To find the count at or below a percentile: multiply the percentile (as a decimal) by total data points.
- Example: For 800 test scores, at the 32nd percentile: 0.32 × 800 = 256 scores at or below.
- To find the count at or above a percentile: subtract the percentile from 100%, convert to decimal, multiply by total.
- Example: For 800 test scores, at or above the 56th percentile: (100% - 56%) = 44%; 0.44 × 800 = 352 scores.
Key Terms & Definitions
- Percentile — The value below which a specified percentage of data falls.
- Quartile — Values that divide data into four equal parts (Q1 = 25th, Q2 = 50th, Q3 = 75th percentiles).
- Median (Q2) — The middle value or the 50th percentile in a data set.
Action Items / Next Steps
- Practice problems calculating percentiles and quartiles.
- Review any assigned textbook readings on percentiles and quartiles.