How do you construct a cumulative frequency table from a data set?

To construct a cumulative frequency table, list data intervals, tally frequencies, and then sum frequencies cumulatively.

First, organise your data into intervals or classes if it isn't already. For example, if you have test scores ranging from 0 to 100, you might create intervals like 0-10, 11-20, and so on. Next, count how many data points fall into each interval. This count is your frequency for each interval.

Now, to find the cumulative frequency, start with the first interval. The cumulative frequency for this interval is just its frequency. For the next interval, add its frequency to the cumulative frequency of the previous interval. Continue this process for all intervals. Essentially, each cumulative frequency is the sum of all previous frequencies up to that point.

For example, if your intervals and frequencies are:
- 0-10: 3
- 11-20: 5
- 21-30: 7

The cumulative frequencies would be:
- 0-10: 3 (just the frequency of the first interval)
- 11-20: 3 + 5 = 8
- 21-30: 8 + 7 = 15

This table helps you see how data accumulates over intervals, making it easier to analyse trends and patterns.