Definition
Frequency polygon and the frequency curve it tends to
Statistics • Frequency Distribution
Statement
A frequency polygon is the figure obtained by plotting each class frequency against that class's mid-point and joining consecutive points by straight line segments, the ends being brought down to the mid-points of the empty classes either side. As the number of observations grows and the classes are made narrower, the plotted points crowd together and the neighbouring frequencies steady, so the polygon tends to a smooth curve — the frequency curve.
How to use it
- 1Plot against class MID-points, not class limits; that is what distinguishes a frequency polygon from an ogive.
- 2The area under a frequency polygon equals the area of the corresponding histogram, so either may be used to compare two distributions.
- 3Read 'what happens as the sample grows' questions as questions about the limiting frequency curve: the answer is smoother, not more jagged.
- 4Few observations spread over few classes is what makes an outline jagged, because one unusually full or empty class moves the whole segment.
Worked example
For the distribution '-: ; -: ; -: ; -: ', name the points a frequency polygon joins.
Step-by-step
- 1
Why: Each class contributes its mid-point as the horizontal coordinate.
- 2
Why: The frequency is the height at that mid-point.
- 3
Why: The empty classes either side bring the polygon down to the axis.
Answer
joined in order
Watch out
A frequency polygon is not an ogive: the ogive plots CUMULATIVE frequency against class boundaries and rises throughout, while the polygon plots the frequency itself against mid-points and may rise and fall.
Builds on
Also known as
frequency polygon, frequency curve, histogram outline, smooth curve limit, polygon of a frequency distribution