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welcome to math with mr j

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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