Mean, Median, and Mode

How to find the mean, median, and mode of a set of numbers.

Find the mean, median, and mode of the following sets of numbers,

and they give us the numbers right over here.

So if someone just says "the mean",

they're really referring to what we typically, in everyday language, call "the average".

Sometimes it's called "the arithmetic mean"

because you'll learn that there are actually other ways of calculating a mean.

But it's really, you just sum up all of the numbers

and you divide by the numbers there are.

And so it's one way of measuring the central tendency

or, you know, the average, I guess we could say.

So this is our mean.

We want to average 23 plus 29,

or we want to sum 23 plus 29 plus 20 plus 32 plus 23 plus 21 plus 33 plus 25

and then divide that by the number of numbers.

So if [counting] 1, 2, 3, 4, 5, 6, 7, 8 numbers.

So you want to divide that by 8.

So let's figure out what that actually is.

Actually, I'll just get the calculator out for this part.

I could do it by hand, but we'll save some time over here.

So we have 23 plus 29 plus 20 plus 20 plus 32 plus 23 plus 21 plus 33 plus 25.

So the sum of all the numbers is 206,

and then we want to divide 206 by 8.

So, if I say 206 divided by 8 gets us 25.75.

So the mean is equal to 25.75.

So this is one way to kind of measure the center, the central tendency.

Another way is with the median. And this is to pick out the middle number.

The median.

And to figure out the median, what we want to do is order these numbers from least to greatest.

So it looks like the smallest number here is 20. Twenty.

Then the next one is 21. Twenty-one.

Then we go... there's no 22 here.

There's uh, let's see here, there's two 23s... 23 and a 23.

So twenty-three and a twenty-three.

And no 24s. There is a 25. Twenty-five.

There's no [counting] 26, 27, 28, there is a 29. Twenty-nine.

And then you have your 32. Thirty-two. And then you have your 33. Thirty-three.

So what's the middle number now that we've ordered it?

So we have [counting] 1, 2, 3, 4, 5, 6, 7, 8 numbers; we already knew that.

And so there's actually going to be two middles.

If you have two... if you have an even number, there's actually two numbers that kind of qualify for

close to the middle, and to actually get the median we're going average them.

So, 23 will be one of them.

That by itself can't be the median,

because there's three less than it, and there's four greater than it.

And 25 by itself can't be the median because there's three larger than it and four less than it.

So what we do is we take the mean of these two numbers and we pick that as the median.

So if you take 23 plus 25 divided by 2, that's 48 over 2 which is equal to 24.

So even though 24 isn't one of these numbers, the median is 24.

So this is the middle number.

So once again, this is one way of thinking about central tendency.

If you wanted a number that could somehow represent the middle,

and I'm going to be clear, there's no one way of doing it.

This is one way of measuring the middle, the middle, let me put that in quotes...

the middle, if you had to represent this data with one number.

And this is another way of representing the middle.

Then finally, we can think about the mode.

And the mode is just the number that shows up the most in this data set.

And all of these numbers show up once except we have the 23 that shows up twice.

And so twenty... since, since because 23 shows up the most,

It shows up twice, every other number only shows up once,

23... 23 is our mode.