3.3 Frequency Histograms 35units are fi ne and the possible values are large, it makes more sense to
treat the data as though it were continuous even though technically it
may be discrete.
3.2 CATEGORICAL DATA
Categorical data is data that is not numerical. Often there is no natural
order to categorical data, although there may be a qualitative ordering,
such as degree of severity. However, if we use a scale such as a Likert
scale to order the categories, they do not have the typical numerical
meaning. For example, a 2 on the scale may not be twice as severe as
- So ratios of the scaled data have no real meaning. Categorical data
can be dichotomous, such as true or false, male or female, yes or no,
alive or dead. It also can consist of three or more categories. So race,
religion, ethnicity, and education level are all examples of categorical
data with more than two categories. Among these four examples, only
education level has a natural ordering in terms of the hierarchy of grade
levels: graduate school > college > high school > elementary school,
for example.
3.3 FREQUENCY HISTOGRAMS
Fo r continuous data, frequency histograms offer us a nice visual
summary of the data and the shape of its distribution. The range of
possible values for the data is divided into disjoint intervals usually of
equal length, and the number of data points in each interval is shown
as a bar. The art of generating frequency histograms is in the decision
as to how many intervals to choose. If you choose too many intervals,
some intervals could be sparse or empty, and the bars could look spikey.
If you take too few intervals, the bars may fl atten and you lose some
of the shape of the distribution.
We shall produce a histogram for a set of body mass index (BMI)
measurements for 120 U.S. adults. The data looks as follows in Table 3.1.
To better discern patterns in this data, it is convenient to order the
data from lowest in the top left corner to highest in the bottom right
corner in ascending order down the columns, for example (could alter-
natively have chosen to go ascending across the rows). The result is
show in Table 3.2.