Cumulative distribution function

The cumulative proportion of values less than or equal to x can be found for any x. They can be shown together in a single graph of the cumulative proportion against x. This is called the cumulative distribution function of the variable.

Annual rainfall in Dodoma

The diagram below shows the cumulative counts for the annual rainfalls in Dodoma.

Drag the vertical red line horizontally and observe that the cumulative count increases by 1 at each data point. Select Cumulative proportion to change the scale on the vertical axis. This is the cumulative distribution function for the rainfall data.

The cumulative distribution function for a data set with n values is a step function that rises from 0.0 at low values of x to 1.0 at high values and increases by 1/n at each value in the data set.