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in this video we're going to go over how

to calculate the variance for a sample

as you see here that notation is s

squared which represents standard

deviation squared or the variance

just getting into the formula we have

the summation of each x

minus the mean squared over n minus 1.

and the sample i'm using only has four

numbers it's 2

5 9 and 12. the reason why i'm choosing

such a small sample is because it's

about the process that matters

when you're calculating it by hand and

that's what i'm showing here this is to

make

to help you understand how the process

goes so that when you have a test

when you are asked about it you know how

to do it whether it's

three five ten numbers the first thing

you have to do is calculate x bar or the

mean

so it's the summation of each x over n

which equals two plus five

plus nine plus twelve over four which

gives you 28 over four

which gives you seven so a nice number

the next thing is to calculate each

x and subtract it from 7 or the mean

square it and then sum them all up so we

have 2 minus 7

squared plus 5 minus 7 squared plus 9

minus 7 squared

plus 12 minus 7 squared

which gives you negative 5 squared plus

negative 2 squared

plus 2 squared plus 5 squared

which gives you 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

finally we get 58 when you add them all

up the last thing here is to just put it

all back into the formula

so we have s squared equals 50 over n

minus 1

which equals 58 over 4 minus 1 which

equals 58 over 3

which equals 19.333 if you wanted the

standard deviation all you'd have to do

is take the square root of 19.33

repeating

and you'd have your standard deviation

for the sample

using these numbers so this process is

obviously very similar to finding the

standard deviation

it's just a matter of where the square

root is so that's why i'm using the same

numbers over and over and over again

because again it's the same process it's

at the end that matters

and it's to help you solidify it in your

head if you're watching each video

i understand from teaching the class

especially those that

may not be majoring in a science or or

math

that it's helpful to use the same

numbers

and then show them where the change is

so it gets solidified in their head if

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