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The Normal Distribution, Clearly Explained!!! - YouTube
Channel: StatQuest with Josh Starmer
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static which makes me crazy when it's
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upside-down stack which makes me bonkers
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when it's upside-down
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stack West hello and welcome to stack
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quest stack quest is brought to you by
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the friendly folks in the genetics
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department at the University of North
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Carolina at Chapel Hill
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today we're going to be talking about
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the normal distribution this is part one
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of a handful of stack quests on this
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distribution because it's so darn
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important today let's just start with
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the basics chances are you've seen a
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normal or Gaussian distribution before
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it's also called
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a bell-shaped curve because it's a
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symmetrical curve that wait for it looks
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like a bell in this example the curve
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represents human height measurements
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people can be short average or tall or
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anywhere in between the y-axis
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represents the relative probability of
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observing someone who is really short or
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really tall or who has an average height
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for example it's relatively rare to see
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someone who is super short
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so the bell-shaped curve is relatively
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low in this part of the graph but it's
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quite common to see someone who is close
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to the average height so the bell-shaped
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curve is very tall in this region and
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it's relatively rare to see someone who
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is really tall so again the bell-shaped
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curve is relatively low in this region
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here are two normal distributions of the
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height of male humans when born and as
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adults this is the distribution for the
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babies and this is the distribution for
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the adults the average baby height is 20
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inches the average adult height is 70
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inches normal distributions are always
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centered on the average value just by
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looking at the graph we can tell there
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is a high probability that a newborn
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baby will be between 19 and 21 inches
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tall
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in contrast adults are between 60 and 80
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inches tall you may have noticed that
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the curve for babies is way tall
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compared to the curve for adults this is
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because there are many more
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possibilities for adult height than for
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babies the more options there are for
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height the less likely any specific
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measurement will be one of them
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the width of the curve is defined by the
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standard deviation we can tell just by
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looking at the curves that babies have a
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relatively small standard deviation
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compared to adults the standard
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deviation for babies is 0.6 the standard
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deviation for adults is 4 knowing the
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standard deviation is helpful because
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normal curves are drawn such that 95% of
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the measurements fall between plus or
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minus two standard deviations around the
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mean
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this means that 95% of the baby
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measurements fall between 20 plus or
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minus 1.2 inches and 95% of the adult
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measurements fall between 70 plus or
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minus 8 inches to draw a normal
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distribution you need to know one
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the average measurement this tells you
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where the center of the curve goes to
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the standard deviation of the
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measurements this tells you how wide the
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curve should be and the width of the
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curve determines how tall it is the
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wider the curve the shorter the narrower
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the curve the taller the curves then
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tell us that there is a high probability
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of measuring a newborn baby boy within
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plus or minus 1.2 inches of the mean
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and there's a low probability of
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measuring a man within plus or minus 1.2
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inches of the mean
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lots of things are normally distributed
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we've been talking about height but
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there's also weight commuting times and
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many many many many many many many more
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things the normal distribution is kind
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of magical in that we see it a lot in
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nature but there's a reason for that and
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that reason makes it super useful for
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statistics as well spoiler alert it's
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called the central limit theorem I'm
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already working on a whole stack quest
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on the central limit theorem so that's
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something we can all look forward to
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hooray
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we've made it to the end of another
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exciting stat quest if you like this
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stat quest and would like to see more of
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them please subscribe and if you have
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any suggestions for stat quests you'd
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like me to do put them in the comments
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below until next time quest on
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