# Cumulative Frequency

- The term ‘cumulative frequency’ refers to the running total of the frequencies in a data set as you move from the lowest to the highest values.
- When collection of data is arranged in ascending order, the cumulative frequency of a value x is the total number of data less than or equal to x.
- To calculate cumulative frequency, you start with the first value (or category if you are working with grouped data) and add the frequency of each subsequent value or category to the total frequency of all previous values/categories.
- Cumulative frequency can assist in estimating median, quartiles and percentiles from a set of data.
- The median is estimated by using the cumulative frequency to identify the middle value in the data set.
- Lower and upper quartiles are found in a similar manner as the median. The lower quartile represents 25% of the data set and the upper quartile represents 75% of the data set.
- Cumulative frequency graphs (also known as ‘ogives’) can be drawn to help visualise and interpret cumulative frequency data.
- On a cumulative frequency graph, the x-axis represents the scores or categories from the data and the y-axis represents cumulative frequency up to and including the score or category.
- The curve of the graph starts at zero and increases as the cumulative frequencies increase.
- Points on a cumulative frequency graph represent the cumulative frequency up to and including the score or category represented by that point on the x-axis.
- Estimations of values - such as the median, quartiles, and percentiles - can be made using a cumulative frequency graph, by plotting the value on the y-axis, and reading the corresponding value on the x-axis.
- The interquartile range (the difference between the upper and lower quartiles) can also be estimated from a cumulative frequency graph, providing a measure of the spread of the data around the median.