18.07 Frequency histograms and polygons

The histogram is a graph that represents the value of a data type using a column. The label underneath the column tells us what score the column refers to while the height of the column tells us the frequency.

In addition to this, a histogram also has labels for both axes that provide information about the axes and tell us what type of values we have.

Consider the histogram below:

We can quickly see that, since the column labelled 1 is the tallest, the mode of the data is 1. We can also see that the column labelled 0 has a value of three, and since column 4 is at the same height, both 0 and 4 have a value of three.

The vertical axis label tells us that the values represent the "number of families" while the horizontal axis label tells us that each column represents a specific "number of children in the family".

Putting this information together, we can see that in the survey there were an equal number of families that had 0 and 4 children; three families in each case.

Examples

Example 1

Create a frequency table using the histogram below.

Worked Solution

Create a strategy

The scores are on the horizontal axis and the frequencies are on the vertical axis.

Apply the idea

Since the bar for 2 goes up to 5, the frequency of 2 is 5. We can find the remaining frequencies in the same way.

Score	Frequency
2	5
3	2
4	6
5	9
6	7
7	9

Watch question walkthrough

Example 2

Find the median for this data set.

Worked Solution

Create a strategy

To find the median using a histogram, find the total number of scores by adding the frequencies for each score.

Apply the idea

\displaystyle \text{Number of scores}	\displaystyle =	\displaystyle 1+5+2+5+1+1	Add the frequencies
	\displaystyle =	\displaystyle 15	Evaluate

There are 15 scores, so the middle scores are the 7th and 8th scores.

We can see that the first 6 scores lie in the first 2 columns. Then the 7th and 8th score lies in the third column which is for the score 6.

This means that both the 7th and 8th score is 6.

\text{Median}=6

Watch question walkthrough

Frequency polygons are like histograms in that they display the scores on the horizontal axis and the frequencies on the vertical axis. We show the frequency of each score by marking the point above the score to the right of the frequency and connecting the points with line segments.

Histogram

Frequency polygon with the same data

Notice that the vertices of the frequency polygon are in the same place as the tops of the bars of the histogram. We can use frequency polygons in the same way that we use histograms.

Examples