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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