Frequency polygons and ogives

Grouped data can be drawn as graphs.

A frequency polygon is a graph of a frequency distribution: frequencies are plotted at the midpoints of the classes and joined by straight lines. It is useful for comparing two or more distributions on one graph.

An ogive is a curve of cumulative frequencies. There are two kinds:

• Less than ogive: cumulative frequencies plotted against the upper limits of the classes. It is a rising curve, starting near zero and ending at N.
• More than ogive: for each class, the number of values more than its lower limit, which is N minus the cumulative frequency below that limit. It is a falling curve, starting at N.

Example: if N = 50 and 12 values lie below 40, then 'more than 40' = 50 − 12 = 38.

The book's own table has two slips in its 'more than' column; work them out yourself from the cumulative frequencies.

The two ogives cross at the median.