Section 2-4
Other types of graphs
 Pareto chart
 time series graph
 pie graph
Pareto Chart
 Used to represent a frequency
distribution for a categorical variable,
and the frequencies displayed by the
heights of vertical bars, which are
arranged in order from highest to lowest.
Pareto Chart
 The table shows the
number of crimes
investigated by law
enforcement officers
in national parks
during 1995.
Construct a Pareto
chart for the data.
 Arrange the data
from the largest to
the smallest
according to
frequency.
 Arrange the data
from the largest to
the smallest
according to
frequency.
 Draw and label x and y axes.
 Draw the bars according to the
frequencies.
Pareto Chart
Suggestions for drawing
Pareto charts
 Make the bars the same width
 Arrange the data from largest to smallest
according to frequency
 Make the units used for the frequency
equal in size
Time series graph
 Represents data that occur over a
specific period of time
 these types of graphs are over 1000
years old. the first ones were used to
chart the movements of the planets and
the sun.
Time series graph
 In 1958 there were
more than 4000
outdoor drive-in
theaters. The
number of theaters
has changed over
the years. Draw a
time series graph for
the data and
summarize the
findings.
Time series graph
 Draw and label the x and y axes
 Label the x axis for years and the y axis
for number of theaters
 Plot each point
 Connect the adjacent points
What can you determine?
When was the biggest drop?
What do you think might have
happened in that time period to
affect drive-ins?
 When you analyze a time series graph,
look for trends. Is the line ascending? Is
the line descending? What is the slope?
Is the rate of change rapid, or slow.
Does it speed up, then slow down?
Does it start slow, then speed up?
Compound time series graph
 When two lines are used. Used for
comparison of data.
This graph shows the number of
snow shovels sold at a hardware
store over two seasons
Pie Chart
 A circle that is divided into sections or
wedges according to the percentage of
frequencies in each category of the
distribution.
Okay, here comes the
math…
 Since there are 360 degrees in a circle,
the frequency for each class must be
converted into a proportional part of the
circle. This conversion is done using a
standard formula.
f
Degrees   360
n
Where f = class frequency and n = total
frequency.
Each frequency must also be
converted to a percentage.
Next, using a protractor and
compass, draw and label the
graph.
Next, using a protractor and
compass, draw and label the
graph.
Misleading Graphs
Graph of an automaker’s claim
 A car manufacturer’s ad stated that 98%
of the vehicles it had sold in the last 10
years were still on the road. The ad
showed a graph similar to this one…
Graph of an automaker’s claim
 Lets consider another example. The
percentage of the world’s total motor
vehicles produced by manufacturers in
the US has declined from 24% in 1998
to 21.5% in 2000, as shown by these
data:
When you look at the graph…
When you change the scale…
When you change the scale…
 Another misleading technique is to
exaggerate a one-dimensional increase
by showing it in two dimensions.
The cost of a Super Bowl ad
The cost of a Super Bowl ad
The cost of a Super Bowl ad
Summary
Histogram
 Used when the data are contained in a
grouped frequency distribution.
Frequency polygon
 Used when the data are contained in a
grouped frequency distribution.
 When not as much “visual pop” is
required.
Ogive
 Used when the data are contained in a
grouped frequency distribution.
 When cumulative frequencies are
desired.
Pareto Chart
 Like a histogram
 Used for nominal or qualitative variables.
Time series graph
 Used to show a pattern or trend that
occurs over a period of time.
Pie graph
 Used to show the relationship between
the parts and the whole.
 Most often uses percentages.
Assignment
read examples 2-12 through 2-14
do exercise set 2-4 1 – 14