Cumulative frequency diagrams can be used to find medians, quartiles, and percentiles.

In the same way that Q1​ is the value greater than a quarter (25%) of data values, the kth percentile is the value greater than k% of the data values.

Example

Since the y-values represent the number of data points with value less than x, and 50% of values are less than the median, it is is the x-value where the line crosses 0.5× the maximum y value on the curve.

Similarly, the quartiles and percentiles are the x-values where the curve crosses:

• Q1​: 0.25× the max

• Q3​: 0.75× the max

• kth percentile: 100k​× the max.