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John Zaixin Zhang

 
 
 

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Equivocation of "Average"  

2010-04-30 23:56:54|  分类: +广告创意与陷阱 |  标签: |举报 |字号 订阅

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Equivocation of “Average”

Depending on different situations (or what results you want to present), an average can be made to look bigger or smaller.

The following example (Bowell 2002) attempting to mislead with statistics includes an equivocation on the meaning of “average,” an average which looks smaller/bigger than the amount of money that the rich/poor could get back in tax reductions.

“These tax reductions will bring real and immediate benefits to middle-income Americans. Ninety-two million Americans will keep an average of $1,083 more of their own money.”

If “average American” means “American with average income”, then this claim is false. What is true is that $1,083 is the average tax reduction under the new plan. But that’s because the highest earners save hundreds of thousands. The American with average income still only gets a few hundred dollars relief. (Note that “American with average income” is tricky too.)

The following is an example of an inflated average (Chesla 1999).

Serenity, Your Dream Hometown

“Looking for a safe, secure place to start a family? Then come to Serenity, Virginia. With an average of ten acres per lot, our properties provide your children with plenty of space to grow and play. Our spacious lawns, tree-lined streets, and friendly neighbors make Serenity a great place to grow up!”

How did Serenity come up with this number?

Here are the facts:

“In Serenity, there are 100 properties. Ten of those properties have 91 acres each. Ninety of those properties have only 1 acre each.”

10 x 91 = 910

90 x 1 = 90

Total acres: 1,000

1,000÷100 (number of properties) = 10 (average acres per property)

But this average doesn’t represent the majority. The typical house in Serenity sits on just one acre, not ten.

In fact, according to Chesla there can be three different averages:

The mean: the value reached by adding the numbers and dividing that total by the number of participants or quantities.

The median: the value that is in the middle: half of the quantities are above and half are below.

The mode: the value that is the most common or that appears the most often.

 

 

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