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

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. 

Misleading Graphs

Brainstorm: What makes a graph misleading???

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?

Why is this graph misleading?This title tells the reader what to think (that there are huge increases in price).

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.

The scale moves from 0 to 80,000 in the same amount of space as 80,000 to 81,000.

A more accurate graph:

An unbiased title

A scale with a regular interval.

This shows a more accurate picture of the increase.

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?

Why is this graph misleading?

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.

The same data: What’s different?

Why might this graph be misleading?

http://sde.state.ok.us/publ/invest00/bench.html

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?

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?

What could be in those iPods besides legally downloaded music?

Empty space – most people don’t 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 person’s iPod is filled with illegal music.

More information: The iPod graphic appeared in Wired magazine. A quote from the article: “What’s 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.

One Last Look:

What makes this pictograph misleading?

Same data: What’s different?

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