Percentile vs Relative Frequency
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Percentile
Describing data
A percentile is a value at or below which a given percentage of the data falls, so about 90 percent of values lie at or below the 90th percentile.
The kth percentile is the value at or below which about percent of the observations lie. For example, if your test score is at the 85th percentile, roughly 85 percent of test-takers scored at or below you. Quartiles are percentiles too: the first quartile is the 25th percentile and the median is the 50th. Percentiles let you compare a single value to a whole distribution without knowing its shape.
Relative frequency
Describing data
A relative frequency is the count in a category divided by the total number of observations, giving a proportion of the whole.
Relative frequency rescales a raw count into a fraction or percent, which makes groups of different sizes comparable. For example, if 18 of 40 students walk to school, the relative frequency is , or 45 percent. The relative frequencies across all categories add up to , that is, 100 percent. This idea is the empirical basis for estimating probabilities from data.