Business Math Series: Averages

The Flaw of Averages

When most people think average, they are thinking of a specific type of average called the arithmetic mean. But there are actually three different types of averages: the mean, median, and mode.

Mean

The arithmetic mean is the most common type of average and it is easy to find. Simply add up your numeric samples and divide by the number of samples. So, for instance, if you are finding the average high temperature of a given week, you would add up the temperature of each day and divide by 7.

Median

Another type of average is called the median. This is the middle ground of all of your samples. So, with the following temperatures in a week you would order them numerically and choose the middle number.

Monday Tuesday Wednesday Thursday Friday Saturday Sunday
35 40 43 51 56 52 49

Doing this for our set we have: 35, 40, 43, 49, 51, 52, 56.

The median temperature for this week, then, was 49.

Mode

The mode is the value that occurs most often. In our case, the values did not repeat and so there is no mode. But if we noted the temperature for an entire season, some high temperatures would repeat. The ones that repeated the most number of times would be the mode.

Range

The range helps us understand how much of a difference there was in our data. You find the range by subtracting your largest number by your smallest. In our example above we would take 56 – 35 = 21. This tells us that there was some variation in temperature. In one week the weather went from being moderate to cold.

Real Life Uses

So, why are there so many different types of averages and what do they mean to the non-mathematical person? All of these different averages are used to help us makes sense of large data sets like, for example, the high temperature of every day in a season. Assuming we record data for 3 months, we will have about 90 weather readings. We can understand the weather patterns by taking the different averages. The mean gives us a feel for what the weather was like over a period of time, the mode tells us what temperature was felt most frequently, and the range tells us if there were any wild swings in the weather.

The usefulness of averages goes way beyond the weather, though. Psychologists use them to make sense of long term research studies. Averages are used to evaluate a player’s performance in sports. Teachers use them to determine how their class is doing overall. Statisticians use them to understand something about a population such as income and education level.

A Rhyme to Remember the Averages

If you can’t remember which is which memorize this rhyme!

Hey diddle diddle,
The median is the middle
You add and divide for the mean
The mode is the one that appears the most
And the range is the difference between

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