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in this video we're going to go over how
to calculate the variance for a sample
as you see here that notation is s
squared which represents standard
deviation squared or the variance
just getting into the formula we have
the summation of each x
minus the mean squared over n minus 1.
and the sample i'm using only has four
numbers it's 2
5 9 and 12. the reason why i'm choosing
such a small sample is because it's
about the process that matters
when you're calculating it by hand and
that's what i'm showing here this is to
make
to help you understand how the process
goes so that when you have a test
when you are asked about it you know how
to do it whether it's
three five ten numbers the first thing
you have to do is calculate x bar or the
mean
so it's the summation of each x over n
which equals two plus five
plus nine plus twelve over four which
gives you 28 over four
which gives you seven so a nice number
the next thing is to calculate each
x and subtract it from 7 or the mean
square it and then sum them all up so we
have 2 minus 7
squared plus 5 minus 7 squared plus 9
minus 7 squared
plus 12 minus 7 squared
which gives you negative 5 squared plus
negative 2 squared
plus 2 squared plus 5 squared
which gives you 25 plus 4 plus 4 plus
25.
remember when it comes to negatives when
you multiply a negative with another
negative you get a positive
finally we get 58 when you add them all
up the last thing here is to just put it
all back into the formula
so we have s squared equals 50 over n
minus 1
which equals 58 over 4 minus 1 which
equals 58 over 3
which equals 19.333 if you wanted the
standard deviation all you'd have to do
is take the square root of 19.33
repeating
and you'd have your standard deviation
for the sample
using these numbers so this process is
obviously very similar to finding the
standard deviation
it's just a matter of where the square
root is so that's why i'm using the same
numbers over and over and over again
because again it's the same process it's
at the end that matters
and it's to help you solidify it in your
head if you're watching each video
i understand from teaching the class
especially those that
may not be majoring in a science or or
math
that it's helpful to use the same
numbers
and then show them where the change is
so it gets solidified in their head if
you found this to be helpful
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and if you suggest it i'll just
make it faster so let me know if you
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