Cumulative proportions

The proportion of values in the data set that are less than or equal to any value, x, is called its cumulative proportion.

For the median and quartiles, the cumulative proportions are:

Value Proportion below
Lower quartile 0.25
Median 0.5
Upper quartile 0.75

The proportion of values greater than x is one minus its cumulative proportion,

Pr(values > x)   =   1 - Pr(values <= x)

Equality

For continuous data, we do not need to distinguish between the proportion of values less than x and the proportion that are less than or equal to x. Provided the values are recorded accurately enough,

However for discrete data (counts) it is important to distinguish the terms 'less than' and 'less than or equal to'.