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SecTIoN 1D Exercises 75

n Mean SD Min Q 1 Med Q 3 Max (b) Based on the boxplot in part (a), what percentage of
Dr. Williams’s students sent more than 64 texts in the
50 3.998 0.739 2.9 3.5 3.85 4.4 7
previous day: less than 25%, between 25% and 50%,
Which measures of center and variability should we between 50% and 75%, or more than 75%? Do the data
choose to summarize this distribution? Explain your confirm Dr. Williams’s suspicion? Explain your answer.
answer. 32. Copper mining In March 2021, a Canadian company
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25. SD contest This is a standard deviation contest. You found substantial deposits of copper at shallow depths in
must choose four numbers from the whole numbers 0 Arizona’s Copper World region, which previously yielded
to 10, with repeats allowed. about 440,000 tons of high-quality copper from 1874 to
1969. The company drilled test holes in several randomly

(a) Choose four numbers that have the smallest possible selected locations at each of the old mine sites, and mea-
standard deviation.
sured the amount of copper (as a percentage) in the rock
(b) Choose four numbers that have the largest possible extracted from each hole. Here are the data from the 28

standard deviation. test holes drilled at the Broad Top Butte site: 85
(c) Is more than one choice possible in either part (a) or

(b)? Explain your answer. 0.00 0.75 1.43 0.43 0.19 0.52 0.00
0.00 0.20 1.38 0.00 0.28 0.71 0.30
26. What do they measure? For each of the following sum-
mary statistics, decide (i) whether it could be used to mea- 0.30 0.44 0.59 0.91 0.33 0.39 0.00
sure center or variability and (ii) whether it is resistant. 0.70 0.37 0.38 0.67 0.00 0.38 0.30

(a) Q 1 + Q 3 (a) Make a boxplot to display the data.
2

(b) An economically viable copper mine has about 0.6%
(b) Max −Min copper in its rock. Based on the boxplot in part (a),
2 what percentage of the rock at Broad Top Butte should
Identifying Outliers the company estimate is more than 0.6% copper: less

27. Soccer outliers Refer to Exercise 1. Use the 1.5 × than 25%, between 25% and 50%, between 50% and
pg 64 IQR rule to identify any outliers in the distribution. 75%, or more than 75%? Explain your answer.
28. Fuel efficiency outliers Refer to Exercise 2. Use the 1.5 × 33. Electoral boxplot Refer to Exercise 5. Here is a box-

IQR rule to identify any outliers in the distribution. plot of the electoral vote data:
29. Cow’s milk outliers Refer to Exercise 23. Determine
whether the distribution has low or high outliers using d d d d
(a) The 1.5 × IQR rule
(b) The 2 × SD rule 0 5 10 15 20 25 30 35 40 45 50 55
30. Country music outliers Refer to Exercise 24. Determine Electoral votes
whether the distribution has low or high outliers using (a) Use the boxplot to estimate the IQR of the distribution.

(a) The 1.5 × IQR rule

(b) Identify an aspect of the distribution that the dotplot in
(b) The 2 × SD rule Exercise 5 reveals that the boxplot does not.
Displaying Summary Statistics: Boxplots 34. Birth rate boxplot Refer to Exercise 6. Here is a box-
31. Daily texts According to blogger Kenneth Burke, plot of the birth rate data:
pg 66 adults ages 18 to 24 send an average of 64 texts per
84
day. Dr. Williams suspected that this value was exag-
gerated, and collected data from a class of Introductory
Statistics students on the number of texts they had sent 10 20 30 40 50
in the past 24 hours. Here are the data: Birth rate (per 1000 individuals)

0 7 1 29 25 8 5 1 25 98 9 0

268 118 72 0 92 52 14 3 3 44 5 42 (a) Use the boxplot to estimate the IQR of the distribution.

(b) Identify an aspect of the distribution that the dotplot in
(a) Make a boxplot to display the data. Exercise 6 reveals that the boxplot does not.

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