Need up to 30 seconds to load.
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
thanks for watching and if you like it
don't forget to subscribe to this
channel
