How can you describe how far apart the
responses are from the center in a data set?
In this lesson you will learn how to
describe the distribution of data by
using the mean absolute deviation.
MAD
First Let’s Review
Reading a dot plot
How many books did 8th graders at Lilburn Middle School read this summer?
0
2
4
6
8
10
12
Number of Books
14
16
18
20
22
Let’s Review
The mean of a set of data is the average.
How many siblings do you have?
0
1
2
3
4
5
0 + 0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 4 + 5 + 5 = 24
24 ÷ 12 = 2
Let’s Review
Absolute value is the distance any number is
from 0.
|-5|
=5
|3|
=3
Variability:
Describes how the spread out or closely
clustered the data set is.
There are 3 ways to determine the spread:
1.Range
2.Interquartile Range
3.Mean Absolute Deviation
A Common Mistake
The mean and mean absolute deviation are often
confused because they both include the word,
“mean.”
Mean
Mean absolute
deviation
Mean Absolute Deviation (MAD):
MAD- is the average distance between each
data value and the mean.
Find the mean absolute deviation.
0
0
How many siblings do you have?
0
1
1
1
2
0
1
2
3
4
5
2
3
Step 1: Find the mean
4
5
+5
24÷12 = 2
2
2
2
1
1
1
0
0
1
2
3
3
Find the mean absolute deviation.
How many siblings do you have?
0
1
2
2
2
2
1
1
1
3
0
0
1 2
4
5
3
3
Step 2 : Find the distance between
the mean and the values |
|
Remember:
Stay positive!
6
5
3 2
lllllllllllllll
3
6 9
12 15
6+3+2+5
MAD=
=4
4
Find the mean absolute deviation.
2
2
How many siblings do you have?
2
1
1
1
0
0
1
2
3
4 5
0
1
3
2
1
0
1 2
3
2
2
1
0
2
1
3
+3
Step
3:
Find
the
average
18 18 ÷ 12 = 1.5
the distance.
of
You can also informally compare
two populations
by using the mean absolute
deviation (MAD).
NFLTeamPenalties
NFC
Mean
92
NFC MAD:
6+33+45+24+21+15+12
7
Distance
AFC
Mean
84
Distance
86
92 – 86=6
80
84-80=4
AFC MAD:
59
92-59=33
67
84-67=17
137
13792=45
114
11484=30
4+17+30+8+10+6+2 =11
7
68
92-68=24
76
84-76=8
113
11392=21
94
94-84=10
77
92-77=15
78
84-78=6
104
10492=12
82
84-82=2
= 22.2
Comparison
The mean absolute deviation for
the NFC is greater than the mean
absolute deviation for the AFC.
That means the data for penalties
for the AFC are closer together.
The NFC has a farther spread.
Guided Practice – Try these two problems
Find the range and mean absolute deviation
of this data.
Find the mean absolute deviation.
How many pets do you have?
0, 1, 5, 0, 3, 1, 0, 2, 2, 6
Race it!!!!
Find the range and mean absolute deviation
of this data.
2
4
6
8
Number of CDs owned
10
12
What is the mean absolute deviation of the
data set?
How many books did you read this summer?
3, 5, 2, 3, 3, 1, 4, 4, 3, 2
What is the mean absolute deviation of the
data set and what does it mean?
How many pairs of shoes do you own?
3, 7, 2, 8, 3, 19, 5, 9
Find the range and mean absolute deviation
of this data.
How many pairs of shoes do 8th graders at
Lilburn Middle School own?