Overview
This lecture explains how to determine the value at the Kth percentile of an ordered data set using a specific formula and provides step-by-step examples.
Finding the Kth Percentile
- Percentiles indicate the value below which a certain percentage of data falls.
- Data set must be ordered from smallest to largest before calculation.
- The formula for the index (I) is: I = (K / 100) × n, where K is the desired percentile and n is the total number of data points.
- If I is not a whole number, always round up to the next whole number to determine the percentile position.
- If I is a whole number, the percentile lies between the Ith value and the next value; take their mean (average).
Example Calculations
- 70th Percentile Example: For n = 28 and K = 70: I = (70/100) × 28 = 19.6; round up to 20th value, which is 62.
- 25th Percentile Example: For n = 28 and K = 25: I = (25/100) × 28 = 7; since 7 is a whole number, find the average of the 7th and 8th values (29 and 30), yielding 29.5.
Rounding Rule
- Always round up if the index (I) is not a whole number, regardless of the decimal value.
Key Terms & Definitions
- Percentile (Kth): The value below which K percent of the data falls.
- Index (I): The position in the ordered list corresponding to the Kth percentile.
- n: Total number of data points in the set.
Action Items / Next Steps
- Practice finding percentiles in various data sets.
- Ensure your data is ordered before applying the formula.