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