how can you describe how far apart the responses are from the center in a data set? in this lesson...
TRANSCRIPT
How can you describe how far apart theresponses are from the center in a data set?
In this lesson you will learn how todescribe the distribution of data by
using the mean absolute deviation.
MAD
0 2 4 6 8 10 12 14 16 18 20 22
Number of Books
First Let’s Review
Reading a dot plot How many books did 8th graders at Lilburn Middle School read this summer?
0 + 0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 4 + 5 + 5 = 2424 ÷ 12 = 2
0 1 2 3 4 5
Let’s Review
The mean of a set of data is the average.
How many siblings do you have?
Let’s Review
Absolute value is the distance any number isfrom 0.
|3| = 3|-5| = 5
Variability:Describes how the spread out or closelyclustered the data set is.
There are 3 ways to determine the spread:
1.Range2.Interquartile Range3.Mean Absolute Deviation
A Common Mistake
The mean and mean absolute deviation are oftenconfused because they both include the word,
“mean.”
MeanMean absolute
deviation
Mean Absolute Deviation (MAD):
MAD- is the average distance between eachdata value and the mean.
00011122345
+524÷12 = 2
Find the mean absolute deviation.
How many siblings do you have?
0 1 2 3 4 5
Step 1: Find themean
222
0 1 2 3 4 5
Find the mean absolute deviation.
How many siblings do you have?
1 2111
33
00
222111001233 Step 2 : Find the distance between
the mean and the values | |
Stay positive!
3 6 9 12 15
3 2
lllllllllllllll
6 5
MAD= 6+3+2+54
=4
Remember:
222
Find the mean absolute deviation.
How many siblings do you have?
0 1 2 3 4 5
33
1 0 1 21 01
22211100123+318 18 ÷ 12 = 1.5
ofStep 3: Find the averagethe distance.
You can also informally compare two populations
by using the mean absolute
deviation (MAD).
NFLTeamPenalties
NFCMean
92Distance
AFCMean
84Distance
86 92 – 86=6 80 84-80=4
59 92-59=33 67 84-67=17
137 137-92=45
114 114-84=30
68 92-68=24 76 84-76=8
113 113-92=21
94 94-84=10
77 92-77=15 78 84-78=6
104 104-92=12
82 84-82=2
NFC MAD:6+33+45+24+21+15+12
7= 22.2
AFC MAD:4+17+30+8+10+6+2
7=11
ComparisonThe 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 deviationof this data.
Find the mean absolute deviation.
How many pets do you have?
0, 1, 5, 0, 3, 1, 0, 2, 2, 6
2 4 6 8 10 12
Number of CDs owned
Race it!!!!
Find the range and mean absolute deviationof this data.
What is the mean absolute deviation of thedata 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 thedata 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 atLilburn Middle School own?