Walking has been shown to be
beneficial not only to our heart and muscles but also to our brain by increasing its
supply of blood. A survey has been conducted in a
secondary school to find out how long students walk per week. The data can be represented with a
relative frequency histogram. Which of the following correctly
displays a relative frequency histogram?
A histogram represents continuous
data. This means that we must have no
gaps between our bars. Therefore, options D and E do not
display a relative frequency histogram. When drawing any histogram, it is
important that we label the axes accurately.
On graph C, despite the bars being
equal width, the gaps between each of the numbers are different. For example, zero to five has a
difference of five, whereas five to 15 has a difference of 10. Between 30 and 45, there is a
difference of 15. As a result of these mistakes, this
graph has been drawn incorrectly and does not display a relative frequency
As the histogram is showing
relative frequency, the height of the bars must sum to one. In graph B, we can see the heights
of the fourth and fifth bar are both greater than 0.5. Adding the heights of these two
bars will give an answer greater than one. This means that graph B also does
not represent a relative frequency histogram as the sum of the height of all the
bars will be greater than one.
This leaves us with graph A. Graph A correctly displays no gaps
for continuous data. The height of all the bars sum to
one. And both of the axes are labelled
This means that the graph that
correctly displays a relative frequency histogram is graph A.