Mentor: Bivariate data is data that involves two different variables whose values can change.
Bivariate data deals with relationships between these two variables. The purpose of bivariate
data is to analyze and explain this relationship.

Student: Is all data bivariate?

Mentor: Actually, some data has only one variable. For example, if I were to record the ages of all
students in a school and graph my data, then there would only be one variable, the age of the
students. This type of data is known as univariate data and it does not deal with
relationships, but rather it is used to describe something. In this example univariate data is
used to express the ages of the students in a school.

Student: OK, so univariate data does not deal with relationships between two things while bivariate
data does?

Mentor: Yes, and since bivariate and univariate data are different, there are different ways of
organizing and examining the data.

Student: What do you mean by "organizing and examining the data"?

Mentor: Well, for example, since univariate data has only one variable we would be interested in
finding a way to summarize information for this single variable. The description of the spread
of the data is one such way that would help us to better understand the data. The spread of a
data set includes the range, median, upper and lower quartiles that divide the data into four
equal sizes, maximum value and minimum value. How do you think understanding spread would be
useful with the example I gave about finding the ages of students in a school?

Student: Well, if we knew the youngest age of students in a school and the oldest age of students in a
school then we would have an idea of what the ages are for all of the students in the school
since each student's age would have to be equal to or between those two ages.

Mentor: Exactly, it is also common to find the mean, median and mode of univariate data sets to
better understand the data. The way that univariate data sets are portrayed graphically is
also different from bivariate data sets. If I wanted to express a univariate data set what
kinds of representations and graphs do you think that I could use?

Student: Well, if finding the median, the quartiles and the range helps us understand the data then
maybe a
box plot would be useful so we could clearly portray that information. However, a box and whisker plot
would only graph the relationship of all of the data together. If I wanted to compare the
amount of students of each age to the amount of students of the other ages then maybe a
bar graph or a
pie graph would be helpful.

Mentor: Yes! Those are several of the many ways to portray univariate information. Now let's switch
our thinking to bivariate data. Since bivariate data includes two variables, and it is used to
examine the relationship between these variables, how do you think we would want to organize
and examine this data? How would you organize the data if one variable represents the amount
of hours you studied for a test and the other variable represents the grade that you received
on the test?

Student: Well, maybe you could make a table with two rows. On the top row you could record the number
of hours studied and on the bottom row the grades that you received, like this:

This way you could see if there is any relationship between the bottom row of variables as the
first row of variables increase. In fact, you could graph this on a coordinate plane if you
label one variable x and the other variable y! If I recorded the data of how many hours I
study for a test in comparison to what grade I make on the test I could have a result such as
the following data set: {(3 hours, 90) (1 hour, 82) (6 hours, 97) (0 hours, 75)}.

Mentor: Good job! You thought of both a visual and a numerical way of organizing and examining the
bivariate data. Both of those ideas could definitely help you understand the data in a
bivariate set. In fact, the graph that you described is commonly used in order to observe a
relationship between data. It is called a
scatter plot. If you would like to explore bivariate data sets more then you can use the
Regression Activity to observe the correlation. Now, we just learned a lot of information, can you sum up what we
learned are the differences between bivariate and univariate data?

Student: OK, we learned that bivariate data has two variables while univariate data has one variable.
We also learned that bivariate data involves relationships between the two variables, while
univariate data involves describing the single variable. We also discussed that information we
would gather from bivariate data would be about the correlation between variables, while the
information we would gather from univariate data would be about its distribution, such as the
range and the mean. Lastly, we discussed that univariate data can be represented in many ways
including a bar graph or a box and whisker plot, while bivariate data is commonly represented
in a scatter plot. Overall, we realized that there are many differences between bivariate and
univariate data!