Section 3.4 ~
A Few Cautions About Graphics
Introduction to Probability and Statistics
Ms. Young ~ room 113
Sec. 3.4
Objective

In this section you will learn how to evaluate graphics
and identify common ways in which graphics can be
misleading
Sec. 3.4
Perceptual Distortions


Sometimes graphics are used to represent an
increase or a decrease over time
The way that they are drawn can distort the
perception of the actual increase or decrease
 Example ~ The following graphics are used to
represent the decrease in the value of a dollar in
comparison to the year 1980

The intention was that the length’s of the dollar bill
would represent the ratio, but our eyes are drawn to the
area of the dollar bill which is very deceiving because it
appears as though it decreased much more than it did
Sec. 3.4
Perceptual Distortions Cont’d…

Example ~ The following graphics are used to represent the
increase in the number of homes with cable television from 1980
to 2005

The intention was that the length’s of the TV’s would represent the
comparison, but our eyes are drawn to the volume of the TV’s which
are very deceiving because it appears as though there was a much
larger increase than there really was
Homes with Cable TV
18 million homes
73 million homes
Sec. 3.4
Watch the Scales

Be cautious that the scales on the horizontal and/or vertical axes are
uniform


If they are not, the graph may be misleading on the first impression
Example ~ The following graph represents the percentage of people owning
their homes from 1960-2005

It appears at first that the years spanning from 1960 to 2000 had a greater
increase in home ownership than the more recent years, but if you look closer,
the horizontal scale is not uniform

The first five categories are a decade apart, but the last two categories are only a
couple years apart
Sec. 3.4
Watch the Scales Cont’d…

Example ~ the following graph represents the percentage of college
students between 1910 and 2005 who were women

It appears as though there was a huge increase of women attending college
after 1950, but if you look at the vertical scale, you should realize that it
does not begin at zero and does not end at 100%

If you redraw the graph with the vertical axis covering the full range from 0%
to 100%, you can see that the increase is not as substantial as it originally
seemed to be.
Sec. 3.4
Exponential Scales

Be cautious about whether the scale is exponential or not

Example ~ the following graph represents the speed of a computer
(calculations per second) from 1950 to 2000

The first graph appears to be increasing linearly, but if you look closer
at the scale, you realize that each tick mark represents a tenfold
increase (grows by a power of 10)

Exponential graph
These exponential scales are useful in displaying data that vary over a huge
range of values
 If you just used an ordinary graph, it makes it very hard to see any
detail in the early years
Ordinary graph
Sec. 3.4
Percentage Change Graphs

If the scale represents percent change (percent increase or percent
decrease), a spike or a drop in the chart doesn’t represent the value
increasing or decreasing, but rather the rate at which it changed

Example ~ the following graph represents the percent change from the
previous year in college costs between private and public colleges


It appears as though the “price” dropped drastically for public colleges after
2004, but really it just means that the percent increase wasn’t as high as it was
in previous years
If you redraw this graph with the actual cost as the scale, you can see that the
cost steadily rises and doesn’t decrease at all
Sec. 3.4
Pictographs

Pictographs are graphs that are enhanced with additional artwork
Although it may make the graph more appealing, it can also distract or
mislead
 Example ~ the following diagram represents the world population from
1804 to 2054



The bars represent the population fairly, but the pictures of people lining the
globe give the impression that the population increases and then falls
In addition to the pictures being misleading, this graph does not use a uniform
horizontal scale, which gives the impression that population has been rising (and
will continue to rise) linearly