The cumulative frequency at the midpoint of an interval refers to the total frequency accumulated up to that specific midpoint.

In statistics, cumulative frequency is a method used to maintain a running total of frequencies across various classes in a frequency distribution table. To determine the cumulative frequency at the midpoint of an interval, you first need to calculate the midpoint itself. This is achieved by adding the lower and upper boundaries of the interval and then dividing the sum by two.

Once the midpoint is established, you can determine the cumulative frequency, which is the sum of all frequencies for the intervals leading up to and including the one that encompasses the midpoint. For instance, if you have intervals representing test scores and their corresponding frequencies, and you wish to find the cumulative frequency at the midpoint of the interval $60-70$, you would start by computing the midpoint:

Next, you would sum all the frequencies from the intervals that are up to and including the $60-70$ interval.

This method provides insights into how data accumulates across a range and is particularly beneficial for constructing cumulative frequency graphs or ogives. These graphical representations can facilitate a better analysis of data distributions. By grasping the concept of cumulative frequency, you can enhance your interpretation of data trends and make more informed decisions based on statistical analysis.