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# Exploring the mean and median

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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.