Bar Charts and Histograms

Like dotplots, bar charts and histograms are used to compare the sizes of different groups.

Bar Charts

A bar chart is made up of columns plotted on a graph. Here is how to read a bar chart.

  • The columns are positioned over a label that represents a categorical variable.
  • The height of the column indicates the size of the group defined by the column label.

The bar chart below shows average per capita income for the four "New" states - New Jersey, New York, New Hampshire, and New Mexico.

Per
Capita
Income
 
$36,000 
$24,000 
$12,000 
 
 
 
 
  New
Jersey
New
Hampshire
New
York
New
Mexico

Histograms

Like a bar chart, a histogram is made up of columns plotted on a graph. Usually, there is no space between adjacent columns. Here is how to read a histogram.

  • The columns are positioned over a label that represents a quantitative variable.
  • The column label can be a single value or a range of values.
  • The height of the column indicates the size of the group defined by the column label.

The histogram below shows per capita income for five age groups.

 
Per
Capita
Income
 
$40,000 
$30,000 
$20,000 
$10,000 
 
 
 
 
 
 25-3435-4445-5455-6465-74

The Difference Between Bar Charts and Histograms

Here is the main difference between bar charts and histograms. With bar charts, each column represents a group defined by a categorical variable; and with histograms, each column represents a group defined by a quantitative variable.

One implication of this distinction: it is always appropriate to talk about the skewness of a histogram; that is, the tendency of the observations to fall more on the low end or the high end of the X axis.

With bar charts, however, the X axis does not have a low end or a high end; because the labels on the X axis are categorical - not quantitative. As a result, it is less appropriate to comment on the skewness of a bar chart.

Test Your Understanding of This Lesson

Problem 1

Consider the histograms below.

6789101112
 
18192021222324

Which of the following statements are true?

I. Both data sets are symmetric.
II. Both data sets have the same range.

(A) I only
(B) II only
(C) I and II
(D) Neither is true.
(E) There is insufficient information to answer this question.

Solution

The correct answer is (C). Both histograms are mirror images around their center, so both are symmetric. The range is equal to the biggest value minus smallest value. Therefore, in the first histogram, the range is equal to 11 minus 7 or 4. And in the second histogram, the range is equal to 23 minus 19 or 4. Hence, both data sets have the same range.