>> In this video, I'm going to talk about the median,
>> In this video, I'm going to talk about the median,

capital M. So the definition of the median is the median
capital M. So the definition of the median is the median

of a data set is the measure of center that is the middle value
of a data set is the measure of center that is the middle value

when the original data values are arranged
when the original data values are arranged

in increasing order.
in increasing order.

Okay. So let's look at some data sets.
Okay. So let's look at some data sets.

First we're going to look at an even data set.
First we're going to look at an even data set.

Okay. The first thing you want to do is you want
Okay. The first thing you want to do is you want

to place the data set in order.
to place the data set in order.

So what's our first number to put it in order?
So what's our first number to put it in order?

Yes 2 then 5 then 7 then 8 and then the other 8,
Yes 2 then 5 then 7 then 8 and then the other 8,

9, 10, 11, 15, and 40.
9, 10, 11, 15, and 40.

Okay. Then what I want to do is I want to find the center.
Okay. Then what I want to do is I want to find the center.

How do we do that?
How do we do that?

Well, we can cross out values starting
Well, we can cross out values starting

from the edges on both sides.
from the edges on both sides.

So let's cross out 2 and 40, 5 and 15.
So let's cross out 2 and 40, 5 and 15.

Work our way in.
Work our way in.

7 and 11, 8 and 10.
7 and 11, 8 and 10.

And you notice that we have 8 and 9 left.
And you notice that we have 8 and 9 left.

If I cross out 8 and 9, I'm not going
If I cross out 8 and 9, I'm not going

to have anything left over.
to have anything left over.

So somehow 8 and 9 is involved in the center, in the median.
So somehow 8 and 9 is involved in the center, in the median.

So what we need to do is to find the average.
So what we need to do is to find the average.

What's between 8 and 9?
What's between 8 and 9?

Well, if we add 8 plus 9 divide by 2, we're going to get 8.5.
Well, if we add 8 plus 9 divide by 2, we're going to get 8.5.

And that is where the median lies.
And that is where the median lies.

Okay. There's another way of determining the median.
Okay. There's another way of determining the median.

And the same thing.
And the same thing.

I'm going to put the values in order.
I'm going to put the values in order.

And I want to know how many values I have
And I want to know how many values I have

so I have 10 values.
so I have 10 values.

Those are the numbers in red.
Those are the numbers in red.

Okay. And to find the median this particular method is I'm
Okay. And to find the median this particular method is I'm

going to use a formula.
going to use a formula.

It's going to be n plus 1 divided by 2.
It's going to be n plus 1 divided by 2.

n says how many data values I have.
n says how many data values I have.

In this case, I know there's 10 of them.
In this case, I know there's 10 of them.

So 10 plus 1 divided by 2.
So 10 plus 1 divided by 2.

That gives me 11 over 2 and that gives me 5.5.
That gives me 11 over 2 and that gives me 5.5.

5.5 what? Well, it turns out that 5.5 is the place
5.5 what? Well, it turns out that 5.5 is the place

where the median is going to be.
where the median is going to be.

That is, it's going to be between 8 and 9.
That is, it's going to be between 8 and 9.

And because of that, we find the average between 8 and 9.
And because of that, we find the average between 8 and 9.

So we add 8 and 9 divided by 2 and we get 8.5.
So we add 8 and 9 divided by 2 and we get 8.5.

So both methods, crossing it out or using the formula, is fine.
So both methods, crossing it out or using the formula, is fine.

It depends on what method your teacher wants you to use
It depends on what method your teacher wants you to use

or what's more comfortable for you.
or what's more comfortable for you.

Okay. Let's look at another example.
Okay. Let's look at another example.

This time the data set will be odd.
This time the data set will be odd.

So what do we do?
So what do we do?

Well, again we want to place the data set in order.
Well, again we want to place the data set in order.

What's our first value?
What's our first value?

That's right 2 then 3, 7, 8, 10, 12, 13 and what else?
That's right 2 then 3, 7, 8, 10, 12, 13 and what else?

And two 16s.
And two 16s.

Okay. So how are we going to find the median?
Okay. So how are we going to find the median?

That's right.
That's right.

Cross it out.
Cross it out.

Cross out the ends on both ends until we find the center.
Cross out the ends on both ends until we find the center.

2 and 16, 3 and 16, 7 and 13, 8 and 12.
2 and 16, 3 and 16, 7 and 13, 8 and 12.

Hey, we got a center of 10.
Hey, we got a center of 10.

Okay. So that's going to be our median which is 10.
Okay. So that's going to be our median which is 10.

So what other way can we do this?
So what other way can we do this?

Well, let's place the data set in order again.
Well, let's place the data set in order again.

And I want to know how many values I have in the data set.
And I want to know how many values I have in the data set.

It seems like I have 9.
It seems like I have 9.

Those are the red numbers.
Those are the red numbers.

So let's use the formula to find the median.
So let's use the formula to find the median.

That's n plus 1 divided by 2.
That's n plus 1 divided by 2.

n is how many values I have in my data set?
n is how many values I have in my data set?

I have 9. So 9 plus 1 divided by 2 gives you 10
I have 9. So 9 plus 1 divided by 2 gives you 10

over 2 which is fifth-place.
over 2 which is fifth-place.

So it's telling me that my median is at the fifth place
So it's telling me that my median is at the fifth place

or the fifth position.
or the fifth position.