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Skewness and symmetry (MEAN, MEDIAN, MODE) - YouTube
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hey there i'm mary the girl who loves
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maths welcome to another lesson
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in this video i'm going to be teaching
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you all about skewed
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and symmetric distributions and how we
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can locate
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the mean median and mode with ease don't
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forget to subscribe to my channel so
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that i can continue to help you out with
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your maths problems
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okay let's go here we have a bell curve
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this curve is considered symmetric which
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means that each side
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is the mirror image of the other you'll
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see that in the center i've identified
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that this is where the mean
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median and mode of the data set lies
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when you're looking at a curve it's
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always easiest to identify where the
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mode lies
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first the mode's just the most repeated
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value so it's always going to be where
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the
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hump or the peak of the curve is
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when we take a look at the mean we need
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to think of it as a set of scales
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and when we think of it as a set of
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scales we need to try and balance
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out the distribution because this
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curve's symmetric the mean lies right in
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the middle
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as it's the same amount of weight on
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each side of the bell
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or if you think of it on each side of
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the scale
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the median is just the middle value of
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the data set where
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half the values lie above the median and
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the other half of the values lie below
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the median
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so the median will also lie in the
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center of this distribution
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let's now go and take a look at a couple
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of skewed distributions
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this is basically when we have some
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extreme values in our data set which
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pull our curve
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to the right or to the left what we're
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looking at here
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is a positively skewed distribution you
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might also call it a right skewed
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distribution
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we call it a positively skewed
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distribution or a right skewed
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distribution
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because this tail here points in the
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positive
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direction or in the right direction this
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is where we have some really extreme
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values being
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pulled to the right so this
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is where we have some really high data
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points
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for example we can think about this as
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the cost of a house
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most houses lie in the hundreds of
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thousands of dollars
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whereas the ones down here on the right
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hand
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right end or the right tail here um
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are really the houses that are in the
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millions and even tens or hundreds of
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millions of dollars right up the far end
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so there are less houses that cost in
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the millions
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and many more houses that cost in the
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hundreds of thousands of dollars range
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now when we take a look at where the
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mean median and mode line this type of
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distribution
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things are going to change a little
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you'll see that our peak
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is further to the left here this is
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where our mode lies
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as it's right where the peak of the
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distribution is
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so the most frequently occurring number
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okay and the mean
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where would the mean lie uh well the
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average which is just the mean
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as it's just the average of a set of
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numbers is going to be dragged
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toward the tail so the means going to be
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dragged
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in the positive direction you could
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think about this as a set of test scores
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one student in the class might score 80
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percent another might score 60
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and another student might only score 10
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if we were to average that out our class
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average would be
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50 for the test however
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if we had an increase in one of the
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scores the final score
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so we've got 80 percent 60 and if the
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final score went up to 75
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that brings our class average to 70 so
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you can see that if
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we're increasing numbers in our data set
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our mean is going to increase as well
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so if we go back up here let's put our
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mean
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i'm going to exaggerate it a little bit
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here but we'll pop our mean here
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as it's going to be pulled in the
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direction of the extreme values
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the median doesn't move as easily as the
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mean it's not as affected by extreme
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values because
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all the median is is the middle value of
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any data set so if there are extra
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values
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in the tail end the median's only going
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to be pushed
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just a little so we can essentially
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pop the median in between the mode and
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the mean
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so in this skewed distribution we have
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the mode
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where the peak of the distribution is
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the mean is always toward the tail end
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the median is always pulled slightly
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toward the tail but
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is not as affected as the mean so it
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sits between
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the mean and the mode let's quickly take
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a look at a negatively skewed
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distribution
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so we have the bulk of our data in here
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and then some extreme values that pull
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our data set this way
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which is why this tail is created moving
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in the negative direction
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to identify our mean median and mode we
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always pop the mode at
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the peak so here is our mode the peak of
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any distribution
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recall that our mean is going to be
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pulled in the direction of the tail
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so let's just pop our mean roughly here
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our median is less affected by the
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extreme low values in this case
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so uh we're going to it still moves in
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the same direction
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as the tail button it's not as
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exaggerated as
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the mean i hope that lesson was
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everything you were looking for please
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make sure you subscribe and ring the
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bell to be notified when i post new
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videos i'll see you in my next lesson
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bye
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