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period we went over two things we talked
about variance which is lowercase Sigma
squared and that equals the summation of
our values minus the mean squared
divided by the number of terms and that
is the variance right now they already
said sixty six point one was the mean
can anybody isalus I just want to make
sure let's just as a let's just double
check that make sure that that is plus
64 plus 64 plus 68 plus 68 plus 69 plus
72 plus 66 divided by how many terms do
we have ten sixty six point one okay so
the mean right and they actually gave it
to Euler problem but I wanted to check
it out the number of values n is equal
to ten and then what we need to do is
take each of these values subtract it
from the mean and then square it
and then add those all up together so
I've sell a lot of students that there
when they're doing these problems we're
not creating tables if you guys remember
when I introduced this I said create a
table that's the easiest thing to do I
know it's a little bit of work but if
you want to be organized and make sure
you get the answer correct
that's what I'd recommend that you go
ahead and do so what we do is just
create we have the table for X sorry and
then the mean then we have X minus the
mean then we have X minus the mean
squared
so let's do that for all of the values
62 63 65 I'm sorry all right
yes 65 doesn't matter if they're in
order 64 64 68 68 69 72 and 66
rich are you back in your seat or you're
supposed to be I can't remember was that
the seat that we moved to or I don't
remember so again the table guys is not
necessary but if you're having trouble
remembering to do this you will be given
the formula but it does take a little
bit of you know work we know that the
mean is sixty six point one and if
anybody can start finding some of these
values that'd be greatly appreciated
especially like the lower valleys I'll
do the first row
but if somebody can maybe start working
from the bottom up I'll start asking
questions so there for the first one I'm
just gonna do 66 are 62 - sixty six
point one I get negative four point one
and then I just square that value and I
get sixteen point eight one does
everybody understand I completed the
first row okay second row now I just do
63 minus 66 so therefore that's going to
be negative three point one then I
square that and I get negative nine
I'm sorry positive nine point six one
then I do
oopsey three and then five so that's
going to be negative one point one and
then negative two point one for the next
one who's that
yeah so one point two one this is
negative two point one negative two
point one and that's squared four point
four one
what is this 1.9 and that one this one's
gonna be 2.9 and that one's going to be
55.9 okay so let's just do these squared
three point six one okay finally
okay does everybody see basically what
we did how we did that so I know for a
couple these problems I mean you guys
had like six I mean you have to it takes
a little bit of work but I'd my
recommendation when I'm coming around
checking your homework is looking to see
that I can see the work it's not
something you can just write in the
answer and I'll say okay you just did
all the standard deviation I mean it
takes some work if you guys do well now
the formula says we need to find the
summation of all of these values so we
need to find the summation of all them
that means we need to add all of these
values so going back to my calculator
sixteen point eight one plus nine point
six one plus one point two one plus four
point four one plus four point four one
plus three point six one plus three
point six one plus eight point four one
plus thirty four point eight one plus
point zero one and as long as I type
them into my calculator correctly which
I'm just going to double check so just
take it slowly just to make sure you
guys do this correctly because you can
miss the decimal points I get so my
variance is equal to the summation which
ends up being eighty six point nine and
therefore then I need to just divide
that by ten cuz ain't by a second to my
value yep so therefore my variance
equals eight point six nine now it's
nice as far as the standard deviation if
you guys remember the formula for
standard deviation standard deviation
equals the square root of the summation
of X minus X million squared over n so
basically all I'm doing is taking the
square root on both sides
so therefore here's the variance if
they're asking me to find the standard
deviation all I need to do is take the
square root of that value and I get nine
point three three or nine point three
two
yeah it's gonna be decimals so just you
can yes going anybody have any questions
on that yes I typed in the wrong number
thank you eight point six nine square
root sorry about that I was looking at
the I took the square root of eighty six
point nine eight point six nine square
root of that is two point nine five
Nathan do you have any questions to make
sense
![A-Level Maths: L3-11 [Data: Introducing the Variance and Standard Deviation]](https://i.ytimg.com/vi/eZB1TdtO7zQ/mqdefault.jpg)
