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Deception with Averages
Using the Difference Types of Average to DeceiveThe use of averages to deceive is a common trick used by statisticians. Deception is achieved by failing to explain whether the average cited is the mean, median, or mode.
Here's a set of numbers:
1, 7, 2, 1, 3
With this set, the mean average is 2.8 (the sum 14 divided by 5).
But the word "average" could also be used to represent the median average. That's the middle-ranked value in the series. To get the median average, you line them all up in order and pick the middle one. Here, it's 2 (which is the middle value in the ordered list of 1, 1, 2, 3, 7). (If there is an even number of numbers in the set and so no obvious middle one, add the middle two, and then divide by two.)
Lastly, the word "average" could be referring to the mode average. That's the most frequently seen number in the set. In this case, it's 1 (which features twice).
Look at these test results:
8%, 8%, 9%, 41%, 70%, 71%, 72%, 74%, 78%, 81%, 82%, 87%, 88%, 89%, 90%, 92%
With the 9% score, I could claim that my score was above average. (I would, of course, be using the mode average when making this claim.)
And what about this claim:
"Half of all doctors are below average in competence."With this claim, the mean average is being used. It's a true statement, but it's a meaningless one. Half of any normally distributed group you choose is below the mean average. But it still sounds bad. There's more fun you can have with this idea. For example, you can disguise the group you're talking about.
"Don't fly with Trower Airlines. It has been statistically proven that half of its pilots are below average."Now, as we're talking about the mean average of all the pilots in Trower Airlines, that's a true but meaningless statistic. But, the connotation here is that a test has been done with every pilot of every airline. If that were actually true, it would not be a meaningless statistic. It would mean Trower Airlines employs below-average pilots when compared with other airlines.
So, why do we need three different kinds of average? Let's take a quick look at each one.
Mean Average. Mean is the most common average, and it's the one that people will think you're talking about if you don't specify which average you're using. Mean average is useful when a central tendency or middle figure is needed, but its weakness is that is can be badly skewed by outliers. For example, it would be useful in measuring the average salary of a group of metal workers in a factory, but it would be less useful in measuring the average salary of everyone in the factory, because the factory owner's and executives' salaries would skew the mean figure. As a result, a senior manager could find himself on a "below average" wage.
Median Average. Median is useful when the distribution has outliers. These are numbers outside the normal set that will skew the mean but will not affect the median. For example, if we were to look at the average age of a school class, the mean will be skewed by the age of the teacher. The median, however, would give us a better idea of the age of the children.
Mode Average. Mode is useful when the things being compared do not have numeric values. If we wished to look at the average bank account held by a group, we could use the mode.
Don't forget the word "average" could have vastly different values for the same group depending on which average the author chooses. Don't think others won't spin this idea to their advantage. It will be used against you, so be on your guard.
Learn more about averages with our sister site, Mathematics Monster.
Understanding Ordinal SetsFinally, before we leave averages, here's a quick word about ordinal sets (that's when data has been ranked in an order). When a newspaper publishes a list of the 10 best films, you cannot say that number 5 is the average "best film". You cannot create a mean from an ordinal set.
Similarly, the top film is not three times better than the third film. There's no relationship between the numbers on the list other than how they're ordered. That seems like an obvious point, but as half the people reading this book are below average (compared to the other half of people reading this book), I thought I'd better spell it out.
Critical Thinking TestAre you good at spotting the biases, fallacies, and other cognitive effects? Can you spot when statistics have been manipulated? Can you read body language? Well, let's see!
- This test has questions.
- A correct answer is worth 5 points.
- You can get up to 5 bonus points for a speedy answer.
- Some questions demand more than one answer. You must get every part right.
- Beware! Wrong answers score 0 points.
- 🏆 If you beat one of the top 3 scores, you will be invited to apply for the Hall of Fame.
- Do you disagree with something on this page?
- Did you spot a typo?
- Do you know a bias or fallacy that we've missed?