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in this video i'm going to teach you how
to calculate variance for a population
the important thing here when it comes
to the formula is understanding the
symbols and where it differs from the
sample variance because on your test you
may just be asked all right well what's
s squared equal what what's sigma
squared equal and you just need to know
the formula at basically is it an n or
is it n minus 1 that you're dividing by
so in this case you have sigma squared
sigma represents
standard deviation sigma squared
represents variance
the variance equals the summation of
each x minus mu
squared over n the population i'm using
is the four numbers i used in my
previous examples with standard
deviation and variance 2 5 9 and 12.
except this is the totality of what
you're looking at not simply a sample
and again that's to emphasize when going
through the process just where the
change is and i'm using the same numbers
so you can see that change if you were
to look at all the answers
for all the different videos the first
thing you need to do if it's not given
to you is calculate mu which is the sum
of each x over n which is
2 plus 5 plus 9 plus 12 over 4 which
equals 28 over 4 which equals 7.
the next thing you need to do is
calculate the summation of each x minus
mu squared
so we got to take 2 minus 7 squared and
then the 5 minus 7 squared and then 9
minus 7 squared and then 12 minus 7
squared and then add them all up
so this is what it gets when you get
simplified you got negative 5 squared
plus negative 2 squared plus 2 squared
plus 5 squared
this yields 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
and then finally you get 58.
the next thing we have to do is just
plug it back into the formula
so we have sigma squared equals 58
over n which is 58 over 4
which
is 14.5 that's not rounding that's just
what the answer is and if you want the
standard deviation for that you just
take the square root of 14.5 this is the
process and how do you get the variance
and ultimately also how you get the
standard deviation if this was helpful
please like and subscribe and i'll catch
you guys later
