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Classifying shapes of distributions | AP Statistics | Khan Academy - YouTube
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what we have here are six different
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distributions and what we're going to do
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in this video is think about how to
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classify them or use the words that
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people typically use to classify
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distributions so let's first look at
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this distribution right over here that's
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the distribution of the lengths of
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housefly so someone went out there and
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measured a bunch of houseflies and then
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said hey look there's many houseflies
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that are between six tenths of a
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centimeter and six and a half tenths of
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a centimeter looks like there's about 40
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houseflies there
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and then if you say between six and a
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half and seven tenths there's about 30
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house flies and if you were to say
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between five and a half tenths and six
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tenths it looks like it's about the same
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amount this type of distribution is
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usually described as being symmetric
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why is it called that
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because if you were to draw a line down
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the middle of this distribution
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both sides look like mirror images of
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each other this one looks pretty exactly
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symmetric but more typically when you're
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collecting data you'll see roughly
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symmetric distributions
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now here we have a distribution that
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gives us the dates on pennies so someone
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went out there observed a bunch of
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pennies looked at the dates on them they
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saw many pennies looks like a little bit
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more than 55 pennies had a date between
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2010 and 2020 while very few pennies had
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a date older than 1980 on them
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and this type of distribution when you
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have a tail to the left
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you can see it right over here you have
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a long tail to the left this is known as
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a left skewed distribution
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left
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skewed
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now in future videos we'll come up with
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more technical definitions of what makes
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it left skewed but the way that you can
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recognize it is you have the high points
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of your distribution on the right but
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then you have this long tail that skews
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it to the left
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now the other side of a left skewed you
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might say well that would be a right
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skewed distribution and that's exactly
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what we see right over here this is a
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distribution of state representatives
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and as you can see most of the states in
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the united states have between 0 and 10
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representatives it looks like it's a
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little over 35 none of them actually
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have zero they all have at least one
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representative but they would fall into
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this bucket while very few have more
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than 50 representatives so here where
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the bulk of our distribution is to the
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left but we have this tail that skews us
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to the right this is known as a right
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skewed
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distribution
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now if we look at this next distribution
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what would this be pause this video and
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think about it
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well this could be a distribution of
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maybe someone went around the office and
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surveyed how many cups of coffee each
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person drank and if they found someone
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who drank one cup of coffee per day
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maybe this would be them and they found
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another person who drinks one cup of
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coffee that's them then they found three
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people who drank two cups of coffee well
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this is a very similar situation to what
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we saw on the dates on pennies
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a large amount of our data fell into
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this right bucket of three cups of
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coffee but then we had this tail to the
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left so this would be left
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skewed
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now these right two distributions are
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interesting one could argue that this
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distribution here which is telling us
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the number of days that we had different
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high temperatures that this is looks
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roughly symmetric or actually even looks
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exactly symmetric because if you did
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that little exercise of drawing a dotted
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line down the middle it looks like the
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two sides are mirror images of each
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other now that would not be technically
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incorrect but typically when you see
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these two peaks this would typically be
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called a bimodal distribution
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so even though bimodal distributions can
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sometimes be symmetric or roughly
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symmetric you want to be more precise
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and here when you have these two peaks
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that's where the buy comes from you
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would call it bimodal and this makes
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sense because
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you have a lot of days that are warm
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that might happen during the summer and
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you might have a lot of days that are
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cold that are happening during the
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winter now this last distribution here
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the results from die rolls
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one could argue as well that this is
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roughly symmetric
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it's not exact it's not perfectly
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symmetric but when you look at this
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dotted line here on the left and the
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right sides it looks roughly symmetric
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but a more exact classification here
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would be that it looks approximately
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uniform so rather than calling it a
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symmetric distribution or a roughly
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symmetric distribution most people would
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classify this as an approximately
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uniform distribution
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