Download Lesson 8-4

Name
Class
Date
Lesson 8-4
Data Variability
Lesson Objective
Common Core Standards
To compare data about two populations
by using measures of center and measures
of variability
Statistics and Probability: 7.SP.3, 7.SP.4
Vocabulary
lower
quartiles.
The mean absolute deviation of a data set measures the average distance from the
mean to each data point.
All rights reserved.
The interquartile range of a set of data is the difference between the upper and
Example
1 Comparing Two Populations A gardener collects information about the
heights of the flowers she grows. Compare the IQRs of the data sets, and
use the comparison to make an inference about the plants.
Salvia
IQR for Salvia:
3
Marigolds
IQR for Marigolds:
18 2 15 5
3
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Height of Plants (in.)
The IQRs of the data sets are the same . So, you can infer that the
heights of Salvia vary about as much as the heights of Marigolds .
Quick Check
1. A
veterinarian collects data about the weights of the dogs she treats. Compare the
medians of the data sets 1, and use the comparison to make an inference about the plants.
Boston Terrier
Australian Terrier
8
© Pearson Education, Inc., publishing as Pearson Prentice Hall.
15 2 12 5
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Weight of Dog (lb)
The
median height of Boston terriers is 6 inches greater than the median
height
for Australian Terriers. Sample answer: Boston terriers are typically
taller
than Australian terriers.
88
441197_C2_Ch8_WKbk_Ver-1.indd 88
Course 2 Lesson 8-4
Daily Notetaking Guide
10/10/12 2:59 PM
Name
Class
Date
Example
2 Determining Overlap of Data Sets The line plot at the right shows
the ages of teens who participated in a junior archery competition.
a. Calculate the mean of each data set.
Girls: Mean 5
150
10
5 15 Boys: Mean 5
170
10
5 17
Participant Ages
Girls
Boys
13
All rights reserved.
b. Determine the MAD for ages of girls in the competition.
Ages
13
18
15
Mean
15 15 15 15 15 15 15 15 15 15
16
Distance
2 2 1 1 0 0 0 1 2 3
17
MAD 5
13
14
14
15
15
total distance
5
number of data items
12
10
15
5
16
6
5
17
14
18
5 1.2
19
c. What number n multiplied by the MAD equals the difference between the
means? What does this number tell you about the overlap of the data sets?
MAD  n 5 difference of means d Write an equation.
1.2n 5 17 2 15 1.2 n 5 2 © Pearson Education, Inc., publishing as Pearson Prentice Hall.
1.2n
1.2
5
2
1.2
n 5 1.67 d Substitute.
d Simplify.
d Divide each side by 1.2 .
Commercials During
Hour-Long Shows
d Simplify.
The difference between the means is 1.67 times the MAD.
The multiple 1.67 is greater than 1, which indicates a small
amount of overlap in the data sets.
Station
A
32
33
Quick Check
34
2.The data table at the right shows the number of commercials during
a random sample of hour-long shows on two television stations.
a. Calculate the mean of each data set.
Station A: 36 Station B: 35
b. Determine the MAD for Station A commercials. 1.2
c. What number n multiplied by the MAD equals the difference
between the means? n  0.83 .
Station
B
35
36
37
38
39
What does this number tell you about the overlap of the data sets?
Sample answer: The difference between the means is 0.83 times the MAD.
Since
0.83 is less than 1, there is a large amount of overlap in the data sets.
Daily Notetaking Guide
441197_C2_Ch8_WKbk_Ver-1.indd 89
Course 2 Lesson 8-4
89
10/10/12 2:59 PM