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[Music]
welcome to math with mr j
[Music]
in this video i'm going to cover mean
absolute deviation
the mean absolute deviation gives us the
average distance between
each number in our data set and the mean
so
how far each number is from our mean
on average and think about it mean means
average
absolute means we're going to be working
with positive distances
and then deviation means something
differs
it's different than the usual so the
average
distance that these numbers differ from
the mean
now the mean absolute deviation gives an
idea
about how much our data differs so how
consistent
or inconsistent it is does the data
differ
greatly is it all close in value or
somewhere
in between this is a measure of spread
it tells us how spread out our data is
let's jump into our example and see
exactly how we do this
the first step that we need to do is
find the mean
so add up all of the numbers and then
divide by how many numbers we have
so let's calculate the mean 3
plus 3 plus 5
plus 8 plus 8
plus twelve so we add all of the numbers
and then divide by how many numbers we
have and we have
six so three plus three is six
plus five is 11 plus 8 is 19
plus 8 is 27 plus 12
gives us 39 and we divide by 6
so 39 divided by 6 gives us
6 and 5 tenths or 6 and a half
so that's our mean once we have that
we can move to the next step so we need
to find
how far each number is from the mean
we do this by finding the absolute value
of
each number minus the mean we want the
absolute value
so we get positive distances now there
are different ways to do this step
as far as setup goes much like most
things in math
i've seen it set up vertically
horizontally or even in tables
whatever works best for you i'm going to
calculate this horizontally
so side to side so let's take each
number
subtract the mean and find the absolute
value of that
and we'll start with three so the
absolute value of three
minus six and five-tenths
plus i'm going to separate each of these
with an addition sign
because looking ahead our next step
we're going to
add these deviations so we have another
3
minus 6 and 5 10
and we will continue our way through our
numbers so a 5 next
now i'm running out of room so i'm going
to go to the
next line down so to speak and we have
an
eight
a couple more here so another eight
and then lastly a 12.
so let's find the absolute value of each
of these
starting with 3 minus six and five
tenths that's going to give us a
negative three and five
tenths the absolute value is going to be
a
positive three and five tenths so i'm
going to make note
above and below these so we have
two of the three minus six and
five-tenths
so now we have five minus six and
five-tenths
that's going to give us a negative one
and
tenths so the absolute value is going to
be
a positive one and five-tenths
eight minus six and five-tenths gives us
a positive one and five-tenths
so the absolute value is a positive one
and five-tenths
same for this eight and then the twelve
twelve minus six and five-tenths gives
us a positive
five and five-tenths so the absolute
value is a positive
five and five-tenths so here
are all of our distances for the numbers
within our data set so their distance
from the mean once we have this
information
we need to find the average of those
distances so we
add them and then divide by the number
of numbers
we have within our data set so those are
steps
3 and 4. so let's add and divide
we'll start by adding so we have three
and five
tenths plus three and five tenths
plus one and five tenths plus
one and five tenths plus one and
five-tenths
plus five and five-tenths
so adding those we're going to get a sum
of
17 so that's our total
amount of distance from the mean if we
add all of our distances
so once we have that let me write 17
here
so we got 17 we need to divide
by the number of numbers within our data
set
and that's going to give us our mean
absolute deviation
so 17 divided by 6.
so 17 divided by 6 is going to give us
an answer of
2.83 and that 3 is going to be repeating
so i'm going to round to the hundredths
place
it's going to give us 2 and 83
hundredths
again the answer is going to be 2.83
and that 3 is going to be repeating so
i'm rounding to the hundredths place
so our mean absolute deviation is 2
and 83 hundredths that's the average
distance
for each of our numbers within the data
set as far as
distance from the mean again this is a
measure of spread so how spread out
are the numbers in our data set now a
very important note here
when comparing or looking at different
mean absolute deviations
the higher the mean absolute deviation
is
the more spread out your data is the
lower the mean absolute deviation is
the closer your numbers are together
so there you have it there's how you
calculate the mean absolute deviation
i hope that helped thanks so much for
watching
until next time peace
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