Understanding Percentiles in Statistics
A percentile is a statistical measure indicating the value below which a given percentage of observations in a group of observations falls. For example, the 20th percentile is the value below which 20% of the observations may be found. Percentiles are widely used in everyday life, from pediatricians plotting a child's height and weight, to universities evaluating SAT or GRE scores.
Percentage vs. Percentile: What's the Difference?
It is common to confuse percentages and percentiles, but they measure completely different things in statistics:
Percentage
A percentage tells you how well you did relative to the test itself. If you score 80% on a test, it means you got 80 out of 100 points possible. It does not take into account how anyone else performed.
Percentile (Percentile Rank)
A percentile tells you how well you did relative to other people who took the same test. If your score is in the 80th percentile, it means you scored equal to or better than 80% of the people who took the test.
How Are Percentiles Calculated?
Finding the Percentile of a Value
To find the percentile rank of a specific score (x), we calculate the percentage of values in the dataset that are strictly less than x, plus half of the values that are exactly equal to x.
Where L = count of numbers less than x, E = count of numbers equal to x, and N = total count of numbers.
Finding the Value at a Percentile
To find the exact value at the k-th percentile, the dataset is first sorted from smallest to largest. An index is calculated based on the desired percentile. If the index falls between two numbers, linear interpolation is used to find the exact value.
Where k = requested percentile, and N = total count of numbers.