Mean Absolute Deviation
So what IS Mean Absolute Deviation?
Mean Absolute Deviation is the mean of the distance of each value from their mean.
(Say What?)
In the definition we see the word “mean” twice. So, YES, we are going to find the mean of the set
of numbers in the data set two times. If you can remember that you find “mean” two times then you
will be over half way to understanding how to find mean absolute deviation.
There are three basic steps in finding mean absolute deviation:
Step 1: Find the “mean” of all of the numbers in your data set.
Step 2: Find the distance of each value from that mean (subtract the mean you found in
step one from each of the original numbers in the data set and ignore the negative sign.)
Step 3: Then find the mean of the distances you found in step 2.
So here is an example for you to follow:
Find the mean absolute deviation of this data set:
3, 6, 6, 7, 8, 11, 15, 16
Step 1: Find the “mean” of all the numbers in your data set.
So to find the “mean” of any set of numbers we add all of the numbers together and
then divide by the total number of the numbers in the data set. Follow the example
below:
So I added all
of my
numbers
from my data
set together.
3 + 6 + 6 + 7 + 8 + 11 + 15 + 16
8
I divided by 8 because there
are 8 numbers total in my
data set.
=
72
8
=9
So 9 is the
mean
(or average)
of the
data set.
Step 2: Find the distance of each value from that mean (subtract the mean from each
value, ignore the negative sign.)
Mean from Step 1:
The average (mean)
of the original set of
numbers in the data set.
Original
data
Original data
minus first mean
Distance
original
number
is from
mean.
3
3-9
6
6
6-9
3
6
6-9
3
7
7-9
2
8
8-9
1
11
11 - 9
15
15 - 9
2
6
16
16 - 9
7
9
3.75
Mean from Step 3:
The average (mean)
of the original set of
numbers in the data set.
Step 3: Find the mean of the last column of numbers (or the distances from the mean).
So in finding the mean absolute deviation we now know how far each number in the data
set is from the average (or mean) of the data set. So on average each data set is 3.75 units
away from the average (or mean) of the original data set. If we drew a picture to
represent this, it would look something like this:
So when we think about mean absolute deviation we can just think of how far (or the
distance) the number is from the average (or mean) of the data set.
Still confused? Here are some web sites that may help:
https://www.youtube.com/watch?v=z9AJk7TvdpQ
https://www.youtube.com/watch?v=USFY2I9VGNQ
Mean Absolute Deviation
Recovery Assignment
Find the mean absolute deviation for each of the following problems. Use your own paper and
show your work. Use the tables on the following sheet.
Problem 1:
The heights of the students in Mrs. Sander’s Kindergarten class, in inches, are:
42, 57, 61, 61, 55, 43, 57, 60, 59, 64
Find the mean absolute deviation of the heights of the students.
Problem 2:
A coach kept a record of how many jumping jacks his fourth grade boys P.E. students could do in one
minute. Their numbers were:
41, 33, 27, 18, 27, 30, 40, 26.
Find the mean absolute deviation of the number of jumping jacks the students could do in a minute.
Problem 3:
A car dealership recorded the number of sales the salespeople had made during the month of October.
The eight salespeople had the following number of sales:
8, 10, 17, 12, 5, 9, 12, 10
What is the mean absolute deviation of the number of sales for the month of October?
Problem 4:
The average gas mileage was recorded for the ten top selling economy cars on the market. The
results were as follows:
42, 41, 38, 44, 43, 37, 48, 36, 36, 41.
What is the mean absolute deviation for the gas mileage of these cars?
Problem Number: _____________
Data
Data minus Mean
Problem Number: _____________
Absolute
Deviation
Problem Number: _____________
Data
Data minus Mean
Data
Data minus Mean
Absolute
Deviation
Problem Number: _____________
Absolute
Deviation
Data
Data minus Mean
Absolute
Deviation