# 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 household income for the four "New" states - New Jersey, New Hampshire, New York, and New Mexico. The chart shows that household income is highest in New Jersey; lowest, in 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. You can see from the chart that per capita income is greatest in the 45 to 54 age group.

## 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 can be 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 not appropriate to comment on the skewness of a bar chart.

Problem 1

Consider the histograms below.  Which of the following statements are true?

I. Both data sets are symmetric.
II. Labels on the X axis are quantitative.

(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. With bar charts, the labels on the X axis are categorical; with histograms, the labels are quantitative. Because these charts were described in the problem statement as histograms, their labels are quantitative.