Cumulative Relative Frequency 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.
Cumulative relative frequency
Describing data
Cumulative relative frequency is the running proportion of the data that falls at or below a given value or category.
Cumulative relative frequency tells you what fraction of the data you have accounted for by the time you reach a certain point, so it rises to 1 as you work through the ordered categories. You compute it as , where is the total number of observations. In a class of 40 students, if 10 scored below 70 and another 14 scored in the 70s, the cumulative count through the 70s is 24 and the cumulative relative frequency is . That 0.60 is also a statement about position: the top of the 70s band sits at roughly the 60th percentile.
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.