Misleading Graphs and Statistics

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Misleading Graphs and Statistics

• PS.1.AC.5 Interpret and evaluate, with and
  without appropriate technology, graphical and
  tabular data displays for consistency with the
  data, appropriateness of type of graph or data
  display, scale, and overall message.
• Students will be able to determine why certain
  graphs are misleading.

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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?

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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.
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A more accurate graph
An unbiased title
A scale with a regular interval.
This shows a more accurate picture of the
increase.
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Why is this graph misleading?
The scale does not have a regular interval.
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Graphs can be misleading in the news.

• The margin of error is the amount (usually in
  percentage points) that the results can be off
  by.
• Be wary of data with large margins of error.

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From CNN.com
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Problems

• The difference in percentage points between
  Democrats and Republicans (and between Democrats
  and Independents) is 8 (62 54). Since the
  margin of error is 7, it is likely that there is
  even less of a difference.
• 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.

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CNN.com updates the graph
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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?
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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.
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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.

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Why is the graph misleading?
Sales of Mango Mango

• What can you say about sales of the drink Mango
  Mango?
• What is decep-tive about the graph?
• How could we change it?

5 4 3 2 1 0







Sales (in 10,000)
Jan Feb
Mar Number of Hours
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Why is the graph misleading?

• If Phils agent says We need to give Phil a
  raise, his hits have doubled since last year!,
  what would be wrong with
  that statement?

Phils Hits

• How could we change this graph so that it is
  not mis-leading?

This year
Last year
0 40 80 120 160 200 240 Hits
0 100 120 140 160 180 200 Hits
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Why do these graphs look different?
Week 1 2 3 4 5
Sales 252 246 265 275 280
330 310 290 270 250 0
500 400 300 200 100 0










Sales
Sales
1 2 3 4 5 Week
1 2 3 4 5 Week