4.5.5 Frequency polygon

A frequency polygon is a type of graph used to represent a frequency distribution of a set of continuous data.

• It is constructed by joining the midpoints of the top of each rectangle in a histogram with straight lines.

• The x-axis represents the range of the data, which is divided into equal intervals or bins, while the y-axis represents the frequency or the number of data points that fall into each bin.

• The frequency polygon can help to visualize the shape of the distribution and identify any patterns or trends in the data.

• In summary, a frequency polygon is a graphical representation of a frequency distribution that shows the frequencies of values in a dataset with connected line segments.

• Some key features of a frequency polygon are

• X-axis : The horizontal axis represents the range of values in the dataset.

• Y-axis : The vertical axis represents the frequency or the number of occurrences of values in the dataset.

• Points : The frequency polygon is constructed by connecting points on the graph. The points are located at the midpoint of the interval on the \( x \)-axis and at the height of the corresponding frequency on the \( y \)-axis.

• Line : The line connecting the points creates a polygon-like shape.

• Shape : The shape of the frequency polygon can provide information about the distribution of the dataset. For example, a bell-shaped curve would indicate a normal distribution.

• Area : The area under the curve of the frequency polygon represents the total number of observations in the dataset.

• Axis labels : The \( x \) and \( y \)-axes are labeled to indicate the units of measurement and the range of values represented on the graph.

• Overall, a frequency polygon is a useful tool for visualizing the distribution of a dataset and identifying patterns in the data.

Worked example:

Let’s say we have a dataset of exam scores for a class of \( 30 \) students.

The scores range from \( 60 \) to \( 100 \) and are given in \( 5 \) point intervals.

Find the midpoint of each interval

Plot the midpoint of each interval on the \( x \)-axis and the frequency on the y-axis.

The resulting graph looks like this:

In this example, the \( x \)-axis represents the score ranges, and the \( y \)-axis represents the frequency of each score range.

The points are connected by a line to form the frequency polygon.

We can see that the highest frequency occurs in the \( 80 \)-\( 84 \) score range, and the distribution of scores is somewhat skewed to the right.

The area under the curve of the frequency polygon represents the total number of exam scores in the dataset, which is \( 30 \) in this example.