how can you describe how far apart the responses are from the center in a data set? in this lesson...

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?