Choose a graph.
Suppose you have quantitative data and you are asked to choose a graph to find the center of
a distribution, or the spread, or the shape.
Notice that here, in the graph, we will ignore what state each observation is from and just look
at the distribution of the numbers.
When we make a graph with a summary of the data to answer some question, often we do not
use all the information in the dataset. We do not use the information that is not relevant to
the question.
Example: In Table 1.4, we see the number of active medical doctors per 100,000 residents in each
state. Make a graph to see the shape of this distribution and estimate the center and spread.
Several choices are possible to correctly answer this. Notice that all of these show the same basic
shape, center, and spread.
Histogram with actual frequencies
Histogram with relative frequencies
(Choose Scale > Y-scale type > Percent )
Histogram of MDs
40
15
30
Percent
Frequency
Histogram of MDs
20
10
20
10
5
0
0
200
300
400
MDs
500
600
Stemplot
200
700
300
Stem-and-leaf of MDs
Leaf Unit = 10
1
2
2
3
3
4
4
5
5
6
6
500
600
700
Dotplot
Stem-and-Leaf Display: MDs
9
(22)
20
8
5
2
1
1
1
1
1
400
MDs
N
= 51
667777999
0000001111222333334444
555555556689
044
678
2
8
Dotplot of MDs
210
280
350
420
MDs
490
560
630
Each of the following is NOT an appropriate graph to answer that question.
Below is a chart which gives the number of MDs by state. This is not a very useful graph to
answer any kind of question. While you can see what the heights of the bars represent, the fact
that there is no really meaningful ordering of the categories (states) here and the fact that there are
so many of them, just about the only thing obvious from this graph is that one has a lot higher
number of MDs than others. You could just as easily have seen that from the numerical data or a
frequency graph (histogram, stemplot, or dotplot.) And the frequency graph would tell you more
useful information too.
Chart of MDs vs state
700
600
MDs
500
400
300
200
100
0
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Below is a chart which gives the number of instances of each possible count of MDs. It is
treating each possible value of “count” as one value of a categorical variable and showing how
many times that value appears. That is useless here. If there were only a few possible values for
the counts of MDs, so we could think of the counts of MDs it was reasonable to think of as a
categorical variable, this might be an useful graph. (Recall problem 1.1 where the individuals
were cars and one variable was the number of cylinders. A bar graph of the number of cylinders
(like this graph) might be interesting for that dataset.
Chart of MDs
3.0
2.5
Count
2.0
1.5
1.0
0.5
0.0
1 3 1 4 6 8 4 6 0 1 2 4 7 8 0 5 9 1 2 8 0 3 6 7 1 2 8 0 1 2 3 6 8 3 5 0 1 5 1 6 0 8 5 7 3
16 16 17 17 17 17 19 19 20 20 20 20 20 20 21 21 21 22 22 22 23 23 23 23 24 24 24 25 25 25 25 25 25 26 26 28 29 30 34 34 36 37 38 42 68
MDs
Summary:
Suppose you have quantitative data and you are asked to choose a graph to find the center of
a distribution, or the spread, or the shape.
The only appropriate choices are frequency graphs, which have the values of the variables along
one axis and the frequencies, or relative frequencies, on the other axis. (Histograms have values of
the variable on the horizontal axis and frequencies up the vertical axis, stemplots have values of the
variable vertically and the “leaves” extend horizontally, giving a visual display of the frequency,
dotplots can be oriented in either direction and aren’t shown in our text, but MINITAB will make
them.)
It is true that these frequency graphs often do not use all the information in the dataset, such as
which individual each observation is from. But that information may not be relevant to answer the
particular question asked, so that’s why we don’t need a type of graph that includes it.
Suppose you have categorical data and you want to choose a graph to illustrate the distribution of
the data. Again, you need a frequency graph. One such graph is a pie chart, and another is a bar
graph, as described in our text. Notice that a bar graph has values of the variable along the
horizontal axis and the frequencies, or relative frequencies, on the vertical axis.