Frequency Polygons
Frequency Polygons
A frequency polygon is sometimes used to represent the same information as in a histogram.A frequency polygon is drawn by using line segments to connect the middle of the top of each bar in the histogram.This means that the frequency polygon connects the coordinates at the centre of each interval and the count in each interval.
Example
Question
Use the histogram from the previous example to draw a frequency polygon of the same data.
Draw the histogram
We already know that the histogram looks like this:
Connect the tops of the rectangles
When we draw line segments between the tops of the rectangles in the histogram, we get the following picture:
Draw final frequency polygon
Finally, we remove the histogram to show only the frequency polygon.
Frequency polygons are particularly useful for comparing two data sets.Comparing two histograms would be more difficult since we would have to draw the rectangles of the two data sets on top of each other.Because frequency polygons are just lines, they do not pose the same problem.
Example
Question
Here is another data set of heights, this time of Grade \(\text{11}\) learners.
\[\begin{array}{l} \text{132}\ ;\ \text{132}\ ;\ \text{156}\ ;\ \text{147}\ ;\ \text{162}\ ;\ \text{168}\ ;\ \text{152}\ ;\ \text{174} \\ \text{141}\ ;\ \text{136}\ ;\ \text{161}\ ;\ \text{148}\ ;\ \text{140}\ ;\ \text{174}\ ;\ \text{174}\ ;\ \text{162}\end{array}\]Draw the frequency polygon for this data set using the same interval length as in the previous example.Then compare the two frequency polygons on one graph to see the differences between the distributions.
Frequency table
We first create the table of counts for the new data set.
| Interval | \((\text{130};\text{140}]\) | \((\text{140};\text{150}]\) | \((\text{150};\text{160}]\) | \((\text{160};\text{170}]\) | \((\text{170};\text{180}]\) |
| Count | \(\text{4}\) | \(\text{3}\) | \(\text{2}\) | \(\text{4}\) | \(\text{3}\) |
Draw histogram and frequency polygon
Compare frequency polygons
We draw the two frequency polygons on the same axes.The red line indicates the distribution over heights for adults and the blue line, for Grade \(\text{11}\) learners.
From this plot we can easily see that the heights for Grade \(\text{11}\) learners are distributed more towards the left (shorter) than adults.The learner heights also seem to be more evenly distributed between \(\text{130}\) and \(\text{180}\) \(\text{cm}\), whereas the adult heights are mostly between \(\text{160}\) and \(\text{180}\) \(\text{cm}\).
This lesson is part of:
Statistics and Probability