Statistics

NZ Level 4

Real Life Data - Misleading Graphs

Lesson

If I told you I came third in a race, you may think I did really well. However, what if there were only three people in the race? Would you still think I did so well?

In a similar way, people use statistics to try and "trick" people into believing their point of view. That's why it's important to understand how to interpret graphs and how people try to bend the rules of graphing.

Did you know?

In 1997, 14-year-old Nathan Zohner, gathered 43 votes from his 50 classmates to ban dihydrogen monoxide. Zohner received the first prize at Greater Idaho Falls Science Fair for analysis of the results of his survey, which was actually convincing people to ban water (H_{2}0)! In recognition of his experiment, journalist James K. Glassman coined the term "Zohnerism" to refer to "the use of a true fact to lead a scientifically and mathematically ignorant public to a false conclusion."

So get your detective skills ready and see if you can spot some suspect stats!

- Cropped graphs: sometimes people use a really small scale on the vertical axis to try and make the differences between groups look bigger. Click here to investigate cropped graphs more.
- Graphs not drawn to scale: remember that the scale (that is measurement units) on the vertical axis are supposed to go up by equal amounts. They may go up in ones, tens or hundreds but if they go up by different amounts or do not even show a scale at all, you should investigate why. Click here for an investigation of graphs not drawn to scale.
- Misleading pictograms: many authors use pictograms to make their statistics more exciting but again, they often do not show an accurate scale to reflect the data. Click here to check out more on pumped up pictograms.
- Graphs with broken axes: scales have to start from zero. However, sometimes the scale needed to do this would make the scale so small that it would be very hard for the reader to notice small but important differences between the bars. Graphs may have broken axes but there are imporant rules to follow. Click here to look at good and bad examples of graphs with broken axes.

Source: *Time Magazine*

The pie chart shows the number of nuclear weapons possessed by each country.

Source: Time Magazine

Considering only the size of the slices (i.e. ignoring the numbers), which of the following countries has the larger nuclear stockpile?

Russia

AUS

BRussia

AUS

BLooking only at the numbers listed for each country, which of the following countries has the larger nuclear stockpile?

US

ARussia

BUS

ARussia

BHas the pie chart been drawn accurately?

Yes

ANo

BYes

ANo

B

Evaluate statements made by others about the findings of statistical investigations and probability activities