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in this video I'm going to talk about

how to calculate the standard deviation

of a set of numbers quick and simple so

the first thing you want to do is

calculate the mean so X bar represents

the mean of the sample and the mean is

basically the sum of the numbers divided

by the size of the sample so we're gonna

add up the five numbers that we have 82

plus 93 plus 98 plus 89 plus 88 and

since we have 5 numbers we are going to

divide this by 5 so 82 plus 93 plus 98

plus 89 plus 88 that gives us a sum of

450 now let's divide that by 5 45

divided by 5 is 9 and if we add a 0 that

gives us an average of 90 so that is our

sample mean now the formula that we're

going to use to calculate the standard

deviation is this formula so we're going

to take the difference of each x value

and the mean and then we're going to

square those differences and take the

sum of those squares and then we're

gonna divide it by n minus 1 so let me

show you how to do that

so the first number is 82 we're going to

subtract that from the mean which is 90

and then square it the next number is 93

we're gonna subtract it from the mean

and then square the mean is 90 and then

it's going to be 98 minus 90 and then

we're gonna keep doing this until it's

finished

so n is 5 and minus 1 is going to be 5

minus 1 or 4 now let's do this one step

at a time

82 minus 90 is negative 8 so this is

gonna be negative 8 squared but once you

square it the negative sign won't matter

and then it's gonna be plus 3 squared 98

- 98-89 minus 90 is negative 1 and so

forth and then divided by 4 so go ahead

and type this in so we have 8 squared

plus 3 squared plus 8 squared plus 1

squared plus 2 squared so that adds up

to 142 divide that by 4 and then take

the square root of that used all and so

you should get a standard deviation of

five point nine five eight so this is

the answer now let's try another example

but one way four more numbers involve so

go ahead and try this calculate the

standard deviation of the numbers I

forgot the S there the numbers shown in

the table below feel free to pause the

video and try it so let's begin by

calculating the sample mean so let's

take the sum of all the numbers so we

have 76 plus 84 plus 69 plus 92 and so

forth so we're gonna take the sum of all

of these numbers and then we're gonna

divide it by the size of the sample so a

next sample we have 10 numbers so n is

10 76 plus 84 plus 69 plus 82 plus 58

plus 89 and this is just a lot of

numbers

let me try that again I think I did that

wrong

so the some of those ten numbers is 800

and if we divide it by ten this will

give us an average of 80 so that's the

sample mean now let's calculate the

standard deviation of the sample so

let's use the same form of that we used

earlier

so it's gonna be the first number 76

minus the mean which is 80 and then

squared and then it's gonna be the next

one which is 84 minus the mean and then

don't forget to square it and then we

need to do this for all of the numbers

so the last one is gonna be 77-82

squared and then divided by n minus one

so we have ten numbers so this is gonna

be ten minus one now if you want to show

all of your work without having to do so

much right in his we could do so notice

that we need to take the difference

between each number and the mean the

difference between 76 and 80 is negative

four but when you square a negative four

it's going to be the same as square and

positive four so we can simply write it

as 4 squared the difference between 84

and 80 is also four so that's going to

be plus another 4 squared 69 is 11 units

away from 80 the next number 92 that's

12 units away from 80 and then 58 if you

do 80 minus 58 that's a difference of 22

and then 89 minus 80,000 civ 9 so you

need to take the squared differences of

each number with the mean 73 minus 80s a

of 797 minus 80 is 1785 minus 80 is 577

minus 80th Street well negative 3 but

we'll make it positive 10 minus 1 is 9

so now it's gonna be easier to calculate

it so 4 squared plus 4 squared plus 11

squared plus 12 squared and so forth

once you add all of the the squared

differences

you should get 1234 so we're going to

divide that number by 9 and then take

the square root of the result so the

standard deviation for this problem is

11 point 7

nine so now you know how to calculate

the standard deviation of a set of

numbers so that's it for this video

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