How to calculate Standard Deviation and Variance - Stastistics Video Lecture - Class 9

in this tutorial I'm going to talk about
calculating the standard deviation in
variance they're both related this isn't
high definition so click on 720 before
you click the fullscreen view the button
right there
a typical problem looks like this the
following are the number of jobs a
sample of six people applied for find
the mean the variance and standard
deviation blah blah blah what you really
are interested in they're just the
numbers and how to calculate the
variance and standard deviation and
that's what I'm gonna do here the sample
standard deviation is equal to the
square root of the sample variance and
these are the symbols I'm going to use
and the first thing I'm going to
calculate is a sample variance the
sample variance is this formula right
here and we'll take the square root of
that to get the standard deviation the X
I that's the observations the x-bar
that's the mean and we'll go through the
calculations of these each one of these
two and n is the sample size I'm going
to make a little table to help me stay
organized and recommend that you do the
same I'm gonna put in the X which did my
observation and then we'll put a little
line horizontal line and I'm gonna do an
up-and-down vertical line as well the
next column is the mean x-bar that's the
mean the sample mean put a little
vertical line as well now I'll just put
in all the observations and that's the
same as above a line and I'm gonna put a
couple more column headings in and
you'll see I'll tell you what those mean
as we fill them in but just go ahead and
write them in now and that's the
observation minus the mean squared so I
need to calculate the mean and that's
equal to the sum of all my observations
divided by the number of observations so
if I add up all my observations that
call them right there that equals 84
now I take that 84 and I put it right on
top of that equation right there and
that's my numerator divided by 6 and ad
equals the my mean which is 14 jobs now
I take that 14 and put it right there in
that column and when the whole column is
gonna be filled with 4 teens now the
next column over is the observation
minus the mean like 17 minus 14 and of
course that is equal to 3 then I have 15
minus 14 that's equal to 1 23 minus 14
that's equal to 9 7 minus 14 that's a
negative 7 9 minus 14 that's negative 5
13 minus 14 that's negative 1 if I add
up this column it should always add up
to 0 always zero that's a good way to
check your numbers 2 now my last column
I take the previous column and I squirt
so 3 squared is 9 1 squared is 1 9
squared is 81 negative 7 squared is 49
doesn't matter if we use a negative sign
or not it's 49 same with 5 squared is 25
negative 1 squared is 1 I drop the
negative sign but it's still always
positive
now I add up this column of information
and it's 166 the 166 is actually the
numerator of this of that equation so
that's the same thing so I can say the
sample variance which I have is s
squared is equal to 166 divided by
divided by n minus 1 n is 6 so it's 6
minus 1 which of course is 5 so the
sample variance is equal to 33 point 2
now if I take that 33 point 2 and take
the square root of that
that's the sample standard deviation
which is equal to s is equal to five
point seven six
now I'll summarize for you the sample
variance is equal to thirty three point
two jobs squared job squared is a unit
sample standard deviation is equal to
five point seven six jobs the sample
mean is equal to fourteen jobs notice
that the standard deviation and sample
mean are in the same units which so they
can be compared with each other as well
and this has just been a slight review
or introduction to calculus standard
deviation and the variance