Really Simple Statistics: Mean, Median, Mode #MRX


Welcome to Really Simple Statistics (RSS). There are lots of places online where you can ponder over the minute details of complicated equations but very few places that make statistics understandable to everyone. I won’t explain exceptions to the rule or special cases here. Let’s just get comfortable with the fundamentals

What is a mean?

There are a few kinds of means that smartie pants like to mention, but most people really are referring to the “average.” Averages are often the easiest way to describe a group using one single number.

For example, the average of
1 1 5 6 7
is
(1+1+5+6+7)÷5=4

Surprisingly, the ‘average’ person does not have ten fingers and ten toes. Because of shop class and accidental dismembering, the average person has FEWER than ten fingers and ten toes. So, this is one case where it doesn’t make sense to talk about averages by using the mean.

What is a median?

The median is the middle number in an ordered list. In other words, half of the numbers are larger and half of the numbers are smaller.

The mean and median often work well together to describe data. If you think about incomes, the average US household income might actually be $500 000 because there is a small group of people who make ridiculously huge salaries (think professional athletes, music and film celebrities, executives of private corporations). But, that average number doesn’t really reflect the salaries that the ‘average’ family earns. So, then we might look at the median US household income which could be $50 000 dollars. Half of people make more than that, and half of people make less than that. Now THAT number makes more sense.

For example, with the same set of numbers…
1 1 5 6 7 … The median is 5
1 6 1 7 5 … The median is still 5
5 1 7 6 1 … And the median is still 5

What is a mode?

Again, people follow me here! I’m not talking about ice cream as in pie ‘a la mode’, though I could really go for some right now!What is the mode?

The mode is the most common number in a list. The mode is useful if you want to say things like “Most people each three meals a day” or “Most people use one bar of soap every week” or “Most people have ten fingers and ten toes.” Using the same list as above, the mode in this list…
1 1 5 6 7 …. is 1.

Really Simple Statistics!

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4 responses

  1. Hey, thanks for ruining my curve (-: Seriously, I am working on a project to rate (automatically) websites on teaching mathematics and statistics. One factor seemed to be blogs vs web pages with blogs disproportionately having flat out incorrect information or being horribly written. And now you have to go do this great post and send me back to the drawing board. Oh well, no one ever gets perfect prediction in real life anyway.

    Picture me slouching away sulking.

    1. Glad to mess up your curve! :)

  2. Cheat sheet: mean = average, median = midpoint, mode = most often:)

    1. That’s a good one!

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