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in this video i'm going to teach you how

to calculate variance for a population

the important thing here when it comes

to the formula is understanding the

symbols and where it differs from the

sample variance because on your test you

may just be asked all right well what's

s squared equal what what's sigma

squared equal and you just need to know

the formula at basically is it an n or

is it n minus 1 that you're dividing by

so in this case you have sigma squared

sigma represents

standard deviation sigma squared

represents variance

the variance equals the summation of

each x minus mu

squared over n the population i'm using

is the four numbers i used in my

previous examples with standard

deviation and variance 2 5 9 and 12.

except this is the totality of what

you're looking at not simply a sample

and again that's to emphasize when going

through the process just where the

change is and i'm using the same numbers

so you can see that change if you were

to look at all the answers

for all the different videos the first

thing you need to do if it's not given

to you is calculate mu which is the sum

of each x over n which is

2 plus 5 plus 9 plus 12 over 4 which

equals 28 over 4 which equals 7.

the next thing you need to do is

calculate the summation of each x minus

mu squared

so we got to take 2 minus 7 squared and

then the 5 minus 7 squared and then 9

minus 7 squared and then 12 minus 7

squared and then add them all up

so this is what it gets when you get

simplified you got negative 5 squared

plus negative 2 squared plus 2 squared

plus 5 squared

this yields 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

and then finally you get 58.

the next thing we have to do is just

plug it back into the formula

so we have sigma squared equals 58

over n which is 58 over 4

which

is 14.5 that's not rounding that's just

what the answer is and if you want the

standard deviation for that you just

take the square root of 14.5 this is the

process and how do you get the variance

and ultimately also how you get the

standard deviation if this was helpful

please like and subscribe and i'll catch

you guys later