>> The next video will be right or left skewed distributions.
It could also be positive or negatively skewed distributions.
Alright, so let's define right skewed distribution.
That's defined as most of the data falls to the left
of the mean and what does that entail?
Well let's draw a right skewed distribution.
And talk about some of its properties.
The first one is let's draw a vertical line
of at the highest point right and this is going
to be the mode, which would be small m. The next one will be
to the right of it, is going to be the median, capital M
and to the next one over that will be the sample mean.
So you can see that for your right skewed distribution you
have the mode, which is the highest point.
The median is in the middle between the mode
and the sample mean and then you have the mean.
Now very quickly here when I say that the mode is the highest,
it doesn't mean the highest in terms of this axis, right.
Sometimes we call it the x. It's not the highest on the x axis.
It's the highest in the y axis right and so that is going
to be very important to understand the difference.
Another way, well of course that's the correct way
of knowing if the distribution is right skewed.
But sometimes by just
if somebody gives you a picture is a right skewed, left skewed
and how would you be able to determine that.
That's not a problem.
Just think of your hand squishing the right side.
If your hand is squishing the right side of the graph,
its right skewed, but that's very very non-mathematical.
Again a true way of determining if it's right skewed or not is
to understand of course the axis right,
the x axis as being larger to the right, smaller to the left.
And understanding that the mode is less than the median,
which is less than the sample mean.
That is the proper way of knowing
if its right skewed or not.
Alright let's move onto the left skewed distribution
and that is most of the data falls to the right of the mean.
Again let's draw a distribution and look
at some of its properties.
And again we know that if we draw the line
at the most data right.
That would be the mode and then on the left
of it would be the median.
And then we have x bar, which is the sample mean.
And again you noticed that the median is
in the middle between the two.
Okay and so sometimes they give you a graph right and they want
to know if its left skewed or right skewed.
Well that's not a problem.
Just think hey, this is squished on the left side, right.
You took your hand and you squished it.
That of course is not a math term or technical
in math jargon, but if you can imagine your hand squishing one
side of the graph, well then its left skewed.
This case it's squashed over here on the left,
but again proper way is to understanding
that you know you have a number line on the x right,
smaller on the left, larger on the right.
And if you take x bar, that's going
to be smaller right, than the median.
And of course smaller than the sample mean.
The median is smaller than the sample mean.
That of course is the proper way of understanding
if the data is left skewed or not.
Okay so let's do some examples.
So again left skewed.
Think of it's very easy to draw a very basic left skewed right.
It's squished which way, left or right?
That's right, left.
So draw a hand on the left and then do couple of bars right,
squished to the left and think about, think about this.
The tallest bar is which one?
That's right, the mode right.
And then of course the middle between any
of these left skewed, right skewed, the middle is what?
Median right and then on the other one must be x bar.
And you know on the x axis from the left it's smaller,
all the way to the right it's bigger.
So, x bar is less than capital M. Alright and less
than small m. Capital no, sample mean is less
than median, less than mode right.
And the next one is right skewed
and again right skewed, where's it squished?
On the left of right?
It's squished on the right, so you draw a hand.
Right and then you do a couple of bars right,
which is the tallest bar, is what?
Mean, median, mode?
That's right, mode.
Then the median because it's the middle between the two
and you have x bar, which is the sample mean.
And you know, again you know that it goes
from left to right, right.
This is small; this is bigger, right or larger right.
So what do we got?
We got mode is less than median is less than x bar.
If you can keep that in your mind,
put it on your sheet right before you take your exam
or your quiz, you'll be fine because any problem
that comes up, you'll be able to do.
So let's do some examples now.
Here's the first one.
Let's say the mode is four and the median is eight
and the sample mean is three.
So we want to know if it's left skewed, right skewed or neither.
It could be neither.
Alright, so let's find out.
The first thing we want to do is we want to put the numbers
in order from small to big.
Three the small one and we're going to put them in order
and we'll also going to put inequality to it.
And it's going to be less than four,
which is the next number, less than what?
What's the next number, eight, right?
We're putting it in with inequalities
because these are the things we need to understand
that that gives us the property of left skewed, right skewed
and we're going to compare that with our problem here.
So we got three, four and eight right, in order.
And they all three is less than four less
than eight, so that's good.
Alright, so three represents what letter
or what central tenancy?
And which is what the sample mean
and its four represents the mode and eight represents the median.
Now question is does this match with right or left skewed?
No, it doesn't and I could've told you already
by the second one.
The second term here, which is the mode.
You notice that in left skewed and right skewed,
the median is in the middle.
So automatically this there was no median in the middle.
So in this case it's going to be neither,
it's going to be neither or neither.
Neither left skewed or right skewed.
Alright, we got the mean is two, the median is four
and the mode is five, so let's put them in order.
Two is less than four, less than five right
and two represents what?
Well that's the mean, that's less than the median right
and five represents the mode.
Well that looks pretty good.
We got the median in the middle, so that's good.
Now we have to match.
Is it right skewed or left skewed?
Well let's see.
This one matches with that one pretty good right
because we got the mean, the median and the mode,
they all match perfect.
So, this one is going to be left skewed.
Alright, let's try the next one
and that example is the median is nine.
The mean is what?
Ten and the mode is three.
Let's put them in order with inequality.
Three represents the mode and nine represents the median
and the ten represents the mean.
That looks pretty good because the median is in the middle,
that's one of the main requirements.
Now question is does this match with any of these?
And it does, it matches with this one.
So this must be right skewed, so this is right skewed.
Alright there is one more,
there is one more example I want to show you.
Well maybe two more.
The median is nine, the mode is seven and the mean is three.
Let's do this, let's put them in order from smaller to large.
Three represents the mean;
seven represents the mode and then the median.
And again the median is not in the middle,
so we automatically know that this is not going to match
with the left skewed or right skewed so this is going
to be neither or neither right.
So that's pretty easy, one more.
This one the median is nine,
the mode is nine and the mean is nine.
Hmm, well that doesn't look good.
It doesn't match with the right skewed or the left skewed,
so this one has a different property.
They're all the same, what does that mean?
What it means that it's symmetrical on nine.
You've probably seen it as a bell curve right, a normal
and because the mean, median
and mode are all the same its symmetrical distribution.
That's a special case and you should be able now
to do left skewed, right skewed top problems
and also symmetrical distribution as well.