Video: Identifying Relative Frequency Histograms

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] Graph A [B] Graph B [C] Graph C [D] Graph D [E] Graph E

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Video Transcript

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 histogram.

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 correctly.

This means that the graph that correctly displays a relative frequency histogram is graph A.

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