Calculating Variance Video Lecture | Mathematics for GRE Paper II

okay in this video I want to talk about
calculating the variance of a set of
data and the variance formula that we
use they label it as s squared and
there's a reason for this because they
talk about the standard deviation being
the square root of variance but anyway
back to the variance it says to
calculate the variance it says X bar
represents the average of your set of
data you have to subtract every value
subtract the the average away from each
value square it and add them up and then
divide by the number of objects in your
sample so in this case consider this
little sample so we have six three eight
five three okay so the first thing
typically that I would do is I would
calculate the average well to calculate
an average we just add up our data six
plus three plus eight plus five plus
three divided by the number which is
five and I got this average to be I
believe I got this to be twenty five
over five so it says the average x-bar
is going to be five okay so maybe I'll
stick that over here to the side so X
bar the average value is going to be
five
okay from that now we have to calculate
so in our formula we have the X of I
minus X bar so all that means is you
take every number and subtract away what
X bar is so 6 minus 5 is 1 I'll take 3
minus 5
I'll take 8 minus 5 5 minus 5 and then
also again 3 minus 5 so let me calculate
that looks like we get negative 2
positive 3 0 and negative 2 so the next
part in our formula it says we have to
add up the sum of the squares
one two in okay well we've got the the
values for each of the squares so now
all we need to do is simply well excuse
me we didn't square yet we now need to
square those so if you take six minus
five squared so six minus five squared
well we calculated what six minus five
is it's one so we'll get one squared
likewise the next value we get when we
square it will get positive four okay so
again all I'm doing is I'm taking every
number that I calculated before and
squaring it if I square three I'll get 9
I squared 0 I get 0 if I square negative
2 I get positive 4 so if I add these
numbers up one plus four plus nine plus
zero plus four I got this to be 18 so
again that's what the Sigma means is it
means to add all the values up okay so
we've done that part now and we're
pretty much there at this point
okay so again it says our formula for
calculating variance
it says the formula is the summation
from I equals 1 to N of each of the
individual points minus the average
squared over the number of objects in
our sample well we just calculated if
you take the each point minus its
average square it add it up we got that
to be the number 18 so that's what we
just calculated on top the number of
objects well we can count 1 2 3 4 5 so
we'll have 5 minus 1 on the bottom or 18
over 4
and it says the variance therefore s
squared is going to equal 4.5 for this
set of data so again all the variance is
somehow it's a measure of the spread of
your data it's just one way to measure
the spread so it basically tells you you
know how close together are your numbers
so here our numbers are sort of close
together so the variance isn't really
big if these numbers were further apart
you could check that you get a larger a
larger number which means they're
varying
more okay so that's the basic idea so I
hope this example helps if you have any
questions feel free to post comments and
hopefully somebody can help you out