Section 3.4 ~ A Few Cautions About Graphics

Introduction to Probability and StatisticsMs. Young ~ room 113

Objective

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In this section you will learn how to evaluate graphics and identify common ways in which graphics can be misleading

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

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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

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Homes with Cable TV

18 million homes 73 million homes

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

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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.

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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)

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

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Exponential graph Ordinary graph

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

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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

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