Misleading Graphs and Statistics

1
Misleading Graphs and Statistics

• Statistical thinking will one day be as necessary
  for efficient citizenship as the ability to read
  and write. H.G. Wells

2
Lesson Objectives

• Students will be able to identify whether graphs
  are misleading. 
• Students will be able to identify the factors
  that make graphs misleading. 
• Students will be able to interpret whose
  interests are favored by misleading graphs. 

3
Misleading Graphs

• Brainstorm
• What makes a graph misleading???

4
Questions to Ask When Looking at Data and/or
Graphs

• Is the information presented correctly?
• Is the graph trying to influence you?
• Does the scale use a regular interval?
• What impression is the graph giving you?

5
Why is this graph misleading?
This title tells the reader what to think (that
there are huge increases in price).
The scale moves from 0 to 80,000 in the same
amount of space as 80,000 to 81,000.
The actual increase in price is 2,000 pounds,
which is less than a 3 increase.
The graph shows the second bar as being 3 times
the size of the first bar, which implies a 300
increase in price.
6
A more accurate graph
An unbiased title
A scale with a regular interval.
This shows a more accurate picture of the
increase.
7
Why is this graph misleading?
The scale does not have a regular interval.
Redraw this graph with a consistent interval.
(Intervals of 1, 2, and 4) Share Out How do the
graphs appear different?
8
Why is this graph misleading?
9
Problems

• Vertical axes dose not start at zero.
• The graph implies that the Democrats were 8 times
  more likely to agree with the decision. In
  truth, they were only slightly more likely to
  agree with the decision.
• The graph does not accurately demonstrate that a
  majority of all groups interviewed agreed with
  the decision.

10
The same data Whats different?
11
Why might this graph be misleading?
http//sde.state.ok.us/publ/invest00/bench.html
12
Problems

• No scale on the vertical axis
• Vertical axis does not start at zero
• Some bars appear to be double in size, when there
  are only small increases

Who might use this graph and why?
13
What does the top of this graph show?

• About 12 million people are downloading music
  legally.
• Just over 9 million people are downloading music
  illegally.

The bottom of the graph is misleading. Why?

• The graph implies that 1 of the iPods are filled
  with legally downloaded music.
• It implies that the other 99 are filled with
  illegally downloaded music.

Why is this wrong?
14
What could be in those iPods besides legally
downloaded music?

• Empty space most people dont have iPods that
  are filled to capacity.
• Songs that were added from legally purchased CDs.
• Games, calendars, other applications.
• Songs that were downloaded illegally.

It is possible that the rest of the iPod contains
some illegally downloaded music, but it is
unlikely that 99 of a persons iPod is filled
with illegal music.
15
More information

• The iPod graphic appeared in Wired magazine.
• A quote from the article Whats filling all
  that excess capacity? Well, despite the efforts
  of the Recording Industry Association of America,
  nearly a billion songs are traded on P2P networks
  every month.
• This article was trying to imply that all of the
  excess space is filled with illegal downloads,
  which is likely untrue.
• The statistics for the article were provided by
  the music industry.

16
One Last Look

• What makes this pictograph misleading?

17
Same data Whats different?
18
Misleading graphs distort the data to create a
false impressions (often called distortions or
exaggerations)

• Some of the most common ways graphs are
  misleading include
• Failing to start axes at 0 or skipping numbers
• Changing the scale of the vertical and/or
  horizontal axis
• Failing to label the axes
• Data is left out
• Icon sizes are not proportional