Here let's take a look at positive and negatively skewed distributions and
we'll also examine the relationship between the three measures of central
tendency in each of those types of distributions.
So our first distribution here is going to look something like this
bear with the slight inaccuracies here due to the pin tablet. We have right here
is one measure of central tendency,
here's a second, and here's a third. They're about evenly spaced they could
vary in practice but the key here is the ordering. OK this first one is
notice how it's the highest point in the distribution here, right?
So that is the mode. The mode is always the highest point in the distribution.
OK then the next one.
Actually let's skip over this one. If you think about the measures
of central tendency, which one is most influenced by the outliers or the
extreme scores over here? Which measure of central tendency in other words is
pulled towards the tail of the distribution?
Well, that is the mean. The mean is the one that is pulled towards the tail.
So it's going to be the furthest to the right. And then that only leaves us with
one more left, right?
That would be the median. So the median is in the middle here.
OK and this type of distribution, if we have a number line here this is the
positive end, this is the negative end.
So remember the skew is determined by where the tail goes.
So the tail here goes to the positive end so this distribution is known
as positively skewed or it has positive skew. Let's look at the other side here.
Here we have the opposite type of distribution. Here's the negative end on a
number line,
here's the positive end. The tail here points to the negative end,
so this is a negatively skewed distribution.
OK the highest point is somewhere around here.
So the highest point's there. So what's this one?
That is the mode, that's I would say the easiest of the three to figure out.
And then we have two more lines here; one here give or take,
and then one here. Look at this one
it's the closest to the tail and that means it's influenced by these
extreme scores. So that would be the mean. And that leaves us with the one that's
in the middle.
That's a clue there. The middle one is the median. The median is the middle
score. And in these two types of distributions it's
going to be the middle measure of central tendency. Let's say that on our
number line here,
this was 10, this was 20, and this was 30.
I'm just making these up but this point here is 10, this point here is 20, and
this point here is 30. And then the same thing here:
10, 20, 30.
OK so the 10 points to the mean, the 20 points to the median, and the 30 here
points to the mode.
OK so in a positively skewed distribution notice how the mean is larger than the
median, which is larger than the mode. So you could say something like this:
the mean is greater than median, which is greater than the mode. In a negatively
skewed distribution it's the opposite:
notice that the mode is the biggest at 30, followed by the median at 20, and then the
mean 10.
So here we have mode greater than median which is
greater than the mean.
OK, that's it. For positively skewed and negatively skewed distributions,
this shows the relationship between the three measures of central tendency.