order to help students focus on the differences between categorical and
numerical data, ask them to think about possible responses to the
following questions and to decide which responses will provide
categorical data and which will provide numerical data:
- How many pets do students in our class have?
- How many hours a week do we spend watching TV?
- What is our favorite sport?
- What kind of music do we like best?
- How many hours a week do we talk on the phone?
- What kinds of snacks do we like?
- How much do our backpacks weigh?
- How much candy do we eat each week?
For this activity students will need to be able to refer to two graphs they created in previous lessons:
Ask students what they notice about the appearance of the two
graphs. They may point out that both are bar graphs (or line graphs).
They may also notice that for the graph on students' heights, there are
numbers along both axes; whereas on the graph about favorite books
(leisure, or TV), there are words along one axis.
Ask students how the data are ordered on each graph. Numerical data
are ordered numerically, but categorical data are ordered arbitrarily.
Unlike the order of numerical data, the order of categorical data can
be changed without affecting the analysis. Because there is no
established order for the arrangement of categorical data, the shape of the data set will vary, depending on the order. Therefore, the shape of the data is not used in the
analysis of categorical data.
Talk with students about how the data sets are analyzed. Since
students have just finished working with numerical data, it is likely
that they will mention the median, range, and outliers. Help students
realize that these measures are used for the analysis of numerical data
but not categorical data. Have them explain why this is so. (The order
of the data can be changed since it is not numerically ordered.) The
mode, on the other hand, does not depend on the order of the data, but
on the frequency, so it can be identified in both categorical and
numerical data. Fractional or proportional relationships can also exist
within both types of data. Throughout this discussion, it is important
that students provide specific examples by referring to the graphs they
created in previous lessons. The students might conclude that
mathematically, there are more ways of talking about numerical data
than about categorical data.