What does cumulative frequency represent in a data set?

Cumulative frequency represents a running total of frequencies up to a certain point in a dataset. It is computed by adding the frequency of each class interval to the sum of the frequencies of all preceding class intervals. This means that for any given data point or class, the cumulative frequency shows how many observations fall within that point or below it, providing insight into the distribution of the data.

For instance, if you have a frequency distribution of scores in a test, the cumulative frequency will tell you how many students scored less than or equal to a specific score. This running total allows for easier analysis of percentiles and quartiles, as well as understanding the overall distribution of data in a more comprehensive way. This is particularly useful in statistics for creating cumulative frequency graphs, which visually represent how data accumulates across intervals or categories.