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Frequency Distributions
and Graphs
Chapter 2
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Other Types of Graphs
2-3
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Bar Graph

A bar graph represents the
data by using vertical or
horizontal bars whose heights
or lengths represent the
frequencies of the data.

A bar graph is used to graph
data from a categorized (or
qualitative) frequency
distribution.
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Bar Graph

How to graph:

For a horizontal bar graph,
write the categories on the
y-axis and the frequency
scale on the x-axis.

For a vertical bar graph,
write the categories on the
x-axis and the frequency
scale on the y-axis.

Draw the bars
corresponding to the
frequencies.
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Compound Bar Graph

A compound bar graph is a
bar graph that compares data
for two or more groups.

The graph on the right
compares data for men and for
women. The bars for each
category (year) for men and
women are placed side by
side.

This allows the reader to
compare data for men versus
women.
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Pareto Chart

A pareto chart is used to
represent a categorical frequency
distribution, and the frequencies
are displayed by the heights of
vertical bars that are arranged in
order from highest to lowest.

How to graph:

The categories are placed on the
x-axis in order from highest
frequency to lowest frequency.

The frequencies are graphed on
the y-axis.
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Time Series Graph

A time series graph
represents data that occur
over a period of time.

How to graph:

The time units are graphed
on the x-axis.

The frequency is graphed
on the y-axis.

Dots are connected but NOT
connected to the x-axis.
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Compound Time Series Graph

Two or more data sets can be
compared at the same time on
a compound time series
graph.
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Pie Graph

A pie graph is a circle that is
divided into sections or wedges
according to the percentage of
frequencies in each category of the
distribution.

How to graph:

Calculate the frequency
percentage for each category.

To calculate the angle measure
of a section:
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Dot Plot

A dot plot is a statistical graph
in which each data value is
plotted as a point (dot) above
the horizontal axis.

A dot plot is used to see how
the data values are distributed
and to see if there are any
extremely high or low data
values.
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Dot Plot

How to graph:

Find the highest and lowest
values to determine the
range of your data.

Draw a horizontal line, and
draw the range (scale) on
the line.

Plot each data value as a dot
above the line.

If the value occurs more
than once, plot the other
point above the first point.
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Stem and Leaf Plots

A stem and leaf plot is a data
plot that uses part of the data
value as the stem and part of
the data value as the leaf to
form groups or classes.

How to graph:
 Arrange the data in order.
 Separate the data according
to the first digit.
 The leading digit is the
“stem” and the trailing digit
is the “leaf”.
 “Leaf” values should be
listed in order.
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Back-to-Back Stem and Leaf Plot

Related distributions can be
compared using a back-toback stem and leaf plot.

The “leaf” values for one data
set is graphed to the left of the
stem. The “leaf” values for the
second data set is graphed to
the right of the stem.
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Misleading Graphs

Inappropriately drawn graphs
can misrepresent data.

Truncating the scale – Notice
that in the top graph, the scale
has been truncated. It shows a
significant difference in data.
The bottom graph is not
truncated – the data are very
similar.
 Changing the units at the
starting point of the y-axis
can convey a very different
visual representation of the
data.
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Misleading Graphs

It is not wrong to truncate an
axis of the graph.
 The bottom graph shows a
slight increase that is barely
detectable in the top graph.
 The point is that you should
check the starting point of
the y-axis when you read a
graph.

Again, changing the starting
point on the y-axis changes
the visual representation. This
is not wrong – we just need to
be aware of it.
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Misleading Graphs

Exaggerating a onedimensional increase by
showing it in two
dimensions: This can make
an increase seem much larger
to the eye than it actually is.

It is not wrong to do this – the
reader should just be cautious
of the conclusions drawn on
the basis of graphs.
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Misleading Graphs

Another way to misrepresent
data on a graph is by omitting
labels or units on the axes.

Without labels and units on the
y axes the graphs below show
little more than a crude
ranking of data.