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  
     
 2534  3544  4554  5564  6574 
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.
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.