Video: Selecting Appropriate Statistical Displays

The following graphs all display data about the pets owned by the students in a class. Which of these displays should we use if we want to analyze the most common type of pet? Which of these displays should we use if we want to compare the number of students who own exactly one pet?

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Video Transcript

The following graphs all display data about the pets owned by the students in a class. Which of these displays should we use if we want to analyse the most common type of pet? And which of these displays should we use if we want to compare the number of students who own exactly one pet?

Both of these graphs display the same data. But different types of graph display different features about that data. Let’s look at the two graphs we’ve been given. The first graph is a bar graph. It shows the type of pet on the horizontal axis. We have cats, dogs, and rabbits. It displays the frequency or the number of students who own each type of pet on the vertical axis. So we can see, for example, that there were 14 students in the class who owned dogs.

The second graph we’ve been given is a Venn diagram. It has a circle to represent each type of pet. Again we have cats, dogs, and rabbits. The numbers in each different section of the Venn diagram tell us how many students owned that particular pet or that particular combination of pets.

For example, these two students here, who were in the circle for cats and the circle for dogs but not the circle for rabbits, are the two students who own both a cat and a dog, but not a rabbit. These two students here who are in the overlap of all three circles own cats, dogs, and rabbits. If we look at the circle for dogs, for example, then we find that the total number of people who own dogs, regardless of whether they own cats, rabbits, or no other pets, is two plus two plus seven plus three. That’s 14, which gives the same number of people who own dogs as we found on the bar graph.

But the two types of graphs have different strengths. If we want to analyse the most common type of pet, then we just need to determine how many students owned each type of pet. We can read these values from the vertical axis of our bar graph. As we’ve just seen, we can also determine these values from our Venn diagram. But we have to perform some addition, finding the sum of the values in each circle. It is therefore easier to analyse the most common type of pet using the bar graph.

If however we want to compare the number of students who own exactly one pet, we won’t be able to do this using our bar graph. We know there are 14 students who own dogs. But we don’t know from the bar graph how many of these also own cats or rabbits.

However, from the Venn diagram, we can see how many students own exactly one pet by looking at the numbers in each circle, which aren’t in the overlaps. We see that there’re six students who own only cats, seven who own only dogs, and four who own only rabbits. Therefore, we need to use the Venn diagram if we want to make comparisons about the number of students who own exactly one pet.

Different types of graphs illustrate different features of a data set. And that’s why it’s important to think about what questions you want to answer before deciding on a particular type of graph to use to represent your data.

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