Average seems like such a simple word. A ‘C’ in a class is average. The average height of a woman is about 5’4″. The average balance for the deposits at your bank can be $5000. The average patient stay at a given hospital is 2.5 days.
These all seem reasonable. But are they?
When you think of average, you probably think back to middle school math and remember that to get the average of a group of figures, you just add them all up and divide that total by the number of figures. So the average of 4,6,8,2,5 = 25 divided by 5 (the number of figures). The answer is 5. In the statistical world, this is called the Mean. When most people hear the word ‘average’, they automatically think of this.
This is very simple. And the value is going to be a good way to generalize about a group of numbers. Or to lie about it…
Let’s Get Mean About The Mean
Let’s look at our examples and see where the Mean makes sense and where we can use it to get some false conclusions:
- A ‘C’ in class is average. This is actually folklore, unless a professor is grading on a very rigid curve, which most do not. Someone averaging a C in college is barely going to graduate. There are definitely more people graduating with A’s than F’s. And at some colleges, like Harvard, the average grade is much higher. ‘C’ just means average in our lexicon. Ruling: TBA
- The average balance for the deposits at your bank is $5000. This number is a little too round to be true and that is because I made it up. But, think about this. You can have 100 customers all with a balance of $5000. Easy math. Or you can have 10 customer with a balance of $40,000 and 90 customers with a balance of about $1100. More likely, the balance will follow a power-law distribution, where the top 10 percent of depositors have well over half the money. So, who is your average customer? You really don’t have one. Ruling: Bogus
- The average height of a woman in the US is about 5’4″. Think of all of the women that you know? How many are 2 feet tall? How many are 28 feet tall? I am going to guess that the number is 0. In fact, most of the women that you know are probably between 5′ and 5’8″. And this group fits a normal distribution (or bell-curve) very nicely. So average is easy to visualize and will not vary much for any random group of women. Ruling: Winner!
- The average patient stay at a given hospital is 2.5 days. This one is similar to the average deposit balance. The vast majority of your patients can be staying 2 days or less, but one 90 patient day stay wrecks all of your numbers. Ruling: Bogus
You can apply a Mean to any group of numbers. That does not always indicate that it is appropriate to use. And it is easy to use to mislead, which is wrong. So don’t do that.
Next we will cover the Median and the Mode, other ways that can be used (and abused) to show an average.