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74 UNIT 1 Exploring One-Variable Data

(b) Suppose the restaurant replaces the burger that has 22 performed in a year by a sample of doctors. Here are

grams of fat with a new burger that has 35 grams of fat. summary statistics for the distribution:
How would this affect the mean and the standard devi-
ation? Justify your answer. x s x Min Q 1 Med Q 3 Max
17. Comparing SD Which of the following distributions 19.1 10.126 5 10 18.5 29 33
has a smaller standard deviation? Justify your answer.
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(a) Find and interpret the interquartile range.

(b) What would you guess is the shape of the distribution
25 25
based only on the summary statistics? Explain your
reasoning.
20 20 Choosing Summary Statistics
Frequency 15 15 pg 61 tics of data on the percentage of butterfat in milk from a
23.
Cow’s milk Here are a histogram and summary statis-
10
10
random sample of 100 three-year-old Ayershire cows: 83
5 5
40
0 0
12345678 12345678 35
Variable A Variable B
30
18. Estimating SD The dotplot shows the number of shots 25
per game taken by National Hockey League (NHL) Frequency
player Sidney Crosby in 81 regular season games in a 20
82
recent season. Is the standard deviation of this distri- 15
bution closest to 2, 5, or 10? Explain your answer with-
out doing any calculations. 10
5
0
3.300 3.591 3.882 4.173 4.464 4.755 5.046
Butterfat (%)

n Mean SD Min Q 1 Med Q 3 Max
100 4.173 0.291 3.52 3.97 4.17 4.37 4.91
Which measures of center and variability should we
choose to summarize this distribution? Explain your
0 2 4 6 8 10
Number of shots answer.
24. Country songs Here are a histogram and summary sta-
Measuring Variability: The Interquartile Range (IQR) tistics of the lengths, in minutes, of 50 songs by country
19. Soccer IQR Refer to Exercise 1. Find the inter- artist Dierks Bentley:
pg 60 quartile range of the distribution.
20. Fuel efficiency IQR Refer to Exercise 2. Find the
interquartile range of the distribution. 16
21. Shopping spree The table displays summary statistics 14
for data on the amount (in dollars) spent by a sample of 12
50 grocery shoppers. 10

x s x Min Q 1 Med Q 3 Max Frequency 8
34.70 21.70 3.11 19.27 27.86 45.40 93.34 6

(a) Find and interpret the interquartile range. 4

(b) What would you guess is the shape of the distribution 2
based only on the summary statistics? Explain your 0
reasoning. 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5
22. C-sections A study in Switzerland examined the num- Song length (min)
ber of cesarean sections (surgical deliveries of babies)

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