Download Data Distributions and Outliers

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LESSON
9-2
Data Distributions and Outliers
Practice and Problem Solving: A/B
For each data set, determine if 100 is an outlier. Explain why or why not.
1. 60, 68, 100, 70, 78, 80, 82, 88
2. 70, 75, 77, 78, 100, 80, 82, 88
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The table below shows a major league baseball player’s season
home run totals for the first 14 years of his career. Use the data
for Problems 3–8.
Season
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Home
Runs
18
22
21
28
30
29
32
40
33
34
28
29
22
20
3. Find the mean and median.
4. Find the range and interquartile range.
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5. Make a dot plot for the data.
6. Examine the dot plot. Do you think any of the season home run totals
are outliers? Then test for any possible outliers.
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7. The player wants to predict how many home runs he will hit in his 15th
season. Could he use the table or the dot plot to help him predict?
Explain your reasoning.
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8. Suppose the player hits 10 home runs in his 15th season. Which of the
statistics from Problems 3 and 4 would change?
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154
showing the data over time, it makes clear
that the player’s home run totals have
fallen back during the past two seasons to
the 18−22 zone.
and his interquartile range is more than
four times as great.
13. Jin is the more consistent test taker. Her
grades show a much smaller range.
8. The mean would decrease to 26.4 and the
median would decrease to 28. The range
would increase to 30 and the interquartile
range would increase to 11.
14. Jin has the standard deviation of 3 and
Brad has the standard deviation of 9.6.
You can tell because Brad’s test scores
are so much more spread out.
Practice and Problem Solving: C
Reading Strategies
1. 100 is not an outlier because Q3 = 89 and
IQR = 17.5.
Then 100 < Q3 + 1.5(IQR).
1. when there is an even number of data
values
2. mean: 8, median: 8.5, range: 12
2. 100 is not an outlier because Q1 = 110
and IQR = 14.
Then 100 > Q1 − 1.5(IQR).
Success for English Learners
1. Possible answer: Problem 1 has an odd
amount of numbers in the set, so there is
a middle. Problem 2 has an even amount
of numbers in the set.
3. mean = 54.15; median = 54
4. range = 27; interquartile range = 7
5.
2. by adding the numbers and then dividing
by how many numbers are present
3. Mean and median would be 5.
4. Patricia forgot to put the numbers in order
from least to greatest first.
6. Possible answer: The line plot makes
clear that there is a cluster of data in
the 51−56 age range. Eleven of the 20
Presidents were in this range upon taking
office. This pattern cannot be seen as
clearly by just looking at the original
data set.
LESSON 9-2
Practice and Problem Solving: A/B
1. 100 is not an outlier because Q3 = 85 and
IQR = 16.
Then 100 < Q3 + 1.5(IQR).
7. Q1 = 51, Q3 = 58, and IQR = 7. So, if a
President’s age upon taking office was less
than 51 − 1.5(7) = 40.5 or greater than 58 +
1.5(7) = 68.5, there is an outlier. From the
line plot, the only outlier is the President
who took office at age 69.
2. 100 is an outlier because Q3 = 85 and
IQR = 9.
Then 100 > Q3 + 1.5(IQR)
3. mean = 27.57; median = 28.5
4. range = 22; interquartile range = 10
8. Possible answer: Because of the cluster
of data in the low 50s and since the mean
and median are close to 54, my guess is
that Cleveland was 54 years old.
5.
6. Possible answer: The dot plot makes it
appear as if 40 is an outlier. However,
since Q3 = 32 and IQR = 10, 40 is not an
outlier since 40 < 32 + 1.5(10)
Practice and Problem Solving:
Modified
1. skewed to the left
2. symmetric
7. Possible answer: The dot plot does not
help predict. It makes it appear that there
are two “zones” where this player tends to
hit home runs: from 18 to 22 and from 28
to 34. The table may help predict. By
3. symmetric
4. skewed to the right
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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