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SecTIoN 1D Exercises 73

(a) Find the mean amount of student loan debt among (b) The one game when the team scored 13 goals is a pos-

U.S. borrowers in 2021. sible outlier in the distribution. Recalculate the range

(b) Do you think the median amount of student loan debt excluding this game. Explain why the result is so differ-
was greater than or less than the mean amount? Justify ent than the answer to part (a).
your answer. 12. Mileage range Refer to Exercise 2.
8. House prices The mean and median selling prices of (a) Find the range of the distribution of highway gas mile-
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existing single-family homes sold in the United States in age for the sample of 21 model-year 2022 midsize cars.
the first 3 months of 2022 were $428,700 and $507,800. 78

(a) Which of these numbers is the mean and which is the (b) The Toyota Prius, with its 48 mpg fuel efficiency, is

a possible outlier in the distribution. Recalculate the
median? Explain your reasoning. range excluding this car model. Explain why the result

(b) What shape would you expect the distribution of home is so different than the answer to part (a).
prices to have? Justify your answer.
9. Teens and fruit We all know that fruit is good for us. Measuring Variability: The Standard Deviation
Here is a histogram of the number of servings of fruit 13. Foot length Here are the foot lengths (in centime-
per day that 74 seventeen-year-olds claimed they con- pg 56 ters) for a random sample of seven 14-year-olds from
79
sumed in a study in Pennsylvania. Find the mean and the United Kingdom:
the median. Show your method clearly.
25 22 20 25 24 24 28
15
Calculate the sample standard deviation. Interpret this
value.
Number of teens 10 first-period statistics class was asked how much sleep (to
14. Well rested? A random sample of 6 students in a

the nearest hour) they got last night. Their responses
were 6, 7, 7, 8, 10, and 10. Calculate the sample stan-
5
dard deviation. Interpret this value.
15. Digital photos How much storage space do digital
0 photos use? Here is a dotplot of the file sizes (to the
0 1 2 3 4 5 6 7 8 nearest tenth of a megabyte) for 18 randomly selected
Servings of fruit per day photos in Noemi’s cloud storage: 81

10. Shakespeare The following histogram shows the dis-
tribution of lengths of words used in Shakespeare’s 1 2 3 4 5 6 7 8
80
plays. Find the mean and the median. Show your File size (mb)
method clearly.

(a) The distribution of file size has a mean of = 3.2x
s

25 megabytes and a standard deviation of = 1.9 mega-
x
bytes. Interpret the standard deviation.
Percentage of words 15 storage space is replaced with another version of the
20
(b) Suppose the music file that takes up 7.5 megabytes of

file that takes up only 4 megabytes. How would this
affect the mean and the standard deviation? Justify your
10
answer.
5 16. Healthy fast food? Here is a dotplot of the amount of
fat (to the nearest gram) in 12 different hamburgers
0 served at a fast-food restaurant:
2 4 6 8 10
Word length
Measuring Variability: The Range 10 15 20 25 30 35 40
Fat content (g)
11. Soccer range Refer to Exercise 1.
pg 55 (a) The distribution of fat content has a mean of = 22.83
x

(a) Find the range of the distribution of goals scored by the

s

U.S. women’s soccer team in all 24 games played that grams and a standard deviation of = 9.06 grams.
x
season. Interpret the standard deviation.
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