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GMAT: Statistical Analysis With Categorical Data
Describing The Relationship Between Two Quantitative Variables

In this video lesson, you will learn about quantitative variables, what they are, and how one variable relates to another. You will learn why this is important and why it can sometimes even save lives.

Describing The Relationship Between Two Quantitative Variables

What Is a Quantitative Variable?

A quantitative variable is something that can be measured and written out as a number. For example, age, height, and life expectancy are all quantitative variables because all of these can be written as a number. If you asked someone to give you their age, they would give you a number. It's the same with the others.

You will see quantitative variables used in surveys. When you have more than one quantitative variable in a survey, relationships between the various variables can be seen. But, why is this important? Why is it helpful to describe the relationships between quantitative variables?

Why Describe Relationships?

Many times, one variable is related to another. Knowing how one variable relates to another gives you valuable information you can use. For example, the two quantitative variables age and height are related to each other. We know that as children age, they also grow taller. We can do surveys on different populations to find out each group's average age-to-height information.

Knowing this can help us. For example, if we are a doctor and we meet a child who happens to be much taller than expected for his age, based on the information we have, we can then proceed to inform his parents and figure out why he is much taller. There could be a medical condition that is causing it. And, if there is, he needs to be treated for it before it causes him damage. If we didn't have our information about the relationship between age and height, then we wouldn't be able to provide this level of help to that child. Knowing how one variable relates to another is important, and it can even save lives.

Let's see how we can come up with a relationship on our own given two quantitative variables and some data collected from a survey.

Two Quantitative Variables

Our two quantitative variables are level of happiness on a scale of 1 to 10, with 10 being the highest level of happiness, and the number of chocolate bars eaten. Both of these are quantitative variables because each is represented by numbers.

We take our little survey to the really nice chocolate bar store at the mall, and we start asking people to rate their level of happiness as they keep eating chocolate bars. We were able to survey 20 people and this is their data:

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How Are They Related?

The best way to figure out how these two variables are related is to use a scatter plot, a graph where you place an individual dot for each data point. We will use the x-axis for our level of happiness and the y-axisfor the number of chocolate bars eaten. Just remember that the level of happiness scale goes from 1 to 10, with 10 being the highest level of happiness. So, if someone put down a 10, that means they enjoyed their chocolate bars the most. If someone put down a 1, then they really weren't happy with the chocolate bars. Let's go ahead and plot our data and see what we find.

Scatter plots are used to find out how variables are related.

This looks rather interesting. I love chocolate, but I do know that if I eat too much, I'll get sick and won't want to see chocolate for a while. The data that we got seems to show that, too. I see that the unhappiest people are the ones that ate a lot chocolate bars, around 10. The happiest people ate only 1 or 2 chocolate bars.

Taking a step back and looking at the whole graph, I see that my dots are loosely following a straight line. This tells me that happiness is related to the number of chocolate bars eaten. If my dots were scattered all over the place, it means that my two quantitative variables are not related to each other. But, if they seem to form a line of some sort, then that means they are related in some way.

For my data, the relationship between the level of happiness and chocolate bars eaten is that the more chocolate bars you eat, the unhappier you will get. If you want to be happy with your chocolate bars, just eat 1 or 2.