SALMAN KHAN: I'm here with our exercise guru Ben Eater.
BEN EATER: Hi Sal.
SALMAN KHAN: And we are looking at this model
you made called Exploring mean and median.
Let's see what it says.
Arrange the five orange points.
So these are the orange points right over here.
On the number line so the arithmetic mean
is negative 0.1.
Arithmetic mean is really kind of what we traditionally
view as the average.
BEN EATER: It's the average.
Yeah.
SALMAN KHAN: You add up the numbers
and divide by the numbers that you have.
And that the median is 2.5.
And 2.5 is essentially the middle number,
if you have an odd number of numbers, which we do here.
BEN EATER: Which we do.
SALMAN KHAN: Or if you have an even number of numbers,
it's the arithmetic mean of the middle two numbers.
It's really going to be--
BEN EATER: --halfway between--
SALMAN KHAN: Halfway between the middle two numbers.
And they're both ways of measuring central tendency.
BEN EATER: Right.
SALMAN KHAN: And the distance between adjacent tick marks
is 1.
So this is like, so this one right over here is 0.
This is 1.
This is 2.
This is negative 1.
This is negative 2.
And so the whole point here-- what's
the point of this exercise?
BEN EATER: The point of it, well, you
said they're both ways of measuring central tendency.
But we can see here is that they don't always
give you the same answer.
So we're being asked to see an arithmetic mean of negative 0.1
and a median of 2.5.
Those are very different numbers.
So how can you take 5 points and say
the central tendency is negative 0.1.
SALMAN KHAN: Right.
BEN EATER: And the central tendency is 2.5.
SALMAN KHAN: Right.
And they're just different ways of measuring it.
BEN EATER: There's different ways of measuring it
and sometimes one way is better than the other.
SALMAN KHAN: Exactly.
BEN EATER: And you kind of have to know.
SALMAN KHAN: I was just starting to play with it
and you see, if I take this the highest number here
and I change it, I can change the mean.
But I didn't change the median because the middle number
is still this middle number, no matter what's
going on out here.
And that's why actually the median
tends to be viewed as a better measure when you have outliers.
When you have really, really, really large values or really,
really, really small values, the median
is a little bit more robust.
So if like this thing is some crazy large number,
the median doesn't change much.
BEN EATER: Right.
SALMAN KHAN: Even though this one number being large
took the whole arithmetic mean up.
Same thing out here.
If I have an outlier over here it doesn't change the median.
BEN EATER: So in this case, it's asking us
a mean of negative 0.1 and a median of 2.5.
Those are very far apart.
SALMAN KHAN: Right.
BEN EATER: So you might expect a lot of outliers.
SALMAN KHAN: Right.
BEN EATER: So when we're done, you probably
would think a lot of the points are going to be closer to 2.5.
SALMAN KHAN: Let's think about this.
Let me get the median first.
So the median is just a middle number.
BEN EATER: Right.
SALMAN KHAN: And so, and here there's 5 numbers
so the middle number literally has to be 2.5.
BEN EATER: So one of those dots has to be on 2.5.
SALMAN KHAN: Let me make the middle number 2.5.
So that gets me to 2.5.
That's got to be--
BEN EATER: You are looking at the mean there.
SALMAN KHAN: Oh sorry.
Yeah, yeah, yeah.
Sorry.
I'm looking at the mean.
2.5 is the median.
Median is 2.5.
And now I want to get the mean at negative 0 point
negative 1, or a negative 0.1.
So let me start making this, let me
see what I can do to make negative.
The mean still is not, so let's see.
Median, look.
There you go.
BEN EATER: There we go.
SALMAN KHAN: There we go.
So let me check my answer.
Yes.
So this you see that there are--
BEN EATER: Yeah, which of those numbers
do you think better represents the central tendency?
SALMAN KHAN: Yeah well.
You--
BEN EATER: I don't know.
SALMAN KHAN: You don't know in this case
I guess it's a, either one is.
Let's see.
If they were all grouped and there was a couple outliers,
then the median probably would've been better.
BEN EATER: Yeah.
And there might be different ways to arrange those dots too.
And you can play with them.
SALMAN KHAN: Yeah, that would be interesting.
Let me check.
I got it right.
Let's do another one.
Next question.
All right.
Arrange the 10 dots.
OK, same thing.
We want the mean 3.6.
Median at 6.
So let me think about the median first.
So I want to get the middle number to median at 6.
The median is six.
BEN EATER: You need to drag one more dot over here
because you're going to be between the two middle numbers
because you have an even number of points.
SALMAN KHAN: Yes, yes, yes.
You're right.
So the median is taking them, right, right, right.
So here we go.
Median is now 6.
BEN EATER: Yep.
SALMAN KHAN: Very good.
Right I had to worry about middle two numbers
because I had an even number.
And now, let me see.
The mean, I need to get to 3.6.
The mean, I need to get to.
And I can't make this one of the middle numbers,
then it'll distort my median.
3 point, I guess it can be one of, it can't get.
BEN EATER: Yeah, you can't go past that number.
SALMAN KHAN: So let's see.
I want to go 3.6.
3.6 gets me right over there.
BEN EATER: There you go.
SALMAN KHAN: There you go.
BEN EATER: So here, which of those numbers
do you think have a better central tendency?
SALMAN KHAN: I would say the median in this one
because this feels a little bit more outlier like.
BEN EATER: Right.
SALMAN KHAN: At least in this situation, the way
I have, we have we've set up this distribution.
Let's check the answer.
That's satisfying.
Get the smiley face.
And you also have hints here if someone has trouble with it.
BEN EATER: That's right.
And they can actually show you maybe a different way to do it.
SALMAN KHAN: So you define the median is the middle number.
Then you show dragging points.
So let's see.
Show us an example.
This is an example where the median and the mean are both 6.
BEN EATER: Right.
So that just puts half the points
to the left of the median and half the points to the right.
SALMAN KHAN: Right, right.
That makes sense.
And then you could keep going.
But that doesn't solve the problem.
BEN EATER: No, it's--
SALMAN KHAN: So let's see.
And then you explain.
So you just give a little more explanation there.
And then finally, you talk about how you changed this
so that you can get the mean of 3.6.
So let's see if you show that example.
So there you go.
BEN EATER: So we just moved a couple of outliers out.
SALMAN KHAN: Outliers affect the mean,
but then the median doesn't change.
Very interesting.