Assignment - Measures of Position and Transformation #1
Student Name : _____________________
Class Name : 4th Per - Prob and Stats Honors
Number of Questions: 17
Instructor Name : CAMPBELL
Question 1 of 17
The following are the distances (in miles) to the nearest airport for
14 families.
9, 11 , 14, 22, 22, 26, 26, 31, 35, 36, 39, 40, 42, 44
Notice that the numbers are ordered from least to greatest.
Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:
Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:
Question 2 of 17
Assignment - Measures of Position and Transformation #1
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Several years ago, the state of California launched an aggressive advertisement campaign against
smoking. We've interviewed students from 18 college campuses in California and recorded for each
campus the percentage of students who stated that they encountered at least one anti-smoking
advertisement in the past month. Here are those percentages.
41, 31, 52, 30, 54, 25, 53, 36, 29, 28, 48, 50, 51, 41, 49, 43, 37, 38
Construct a box-and-whisker plot for the data.
25
30
35
40
45
50
Percentage encountering anti-smoking ad
Question 3 of 17
Assignment - Measures of Position and Transformation #1
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A golfer recorded the score for each round of golf she played in a season. The box-and-whisker plot
(sometimes called a boxplot) summarizes these scores.
60
65
70
75
80
85
90
95
100
Score
Use the box-and-whisker plot to answer the following.
(a) What is the median score?
__________
(b) What is the lowest score?
__________
(c) What is the first quartile (Q1) of the scores?
__________
Question 4 of 17
The last
10 calls to a customer support line had the following lengths (in minutes).
53, 54, 55, 57, 58, 60, 60, 62, 63, 66
Complete the parts below to identify any outliers.
Assignment - Measures of Position and Transformation #1
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(a)
Let
Q1 be the lower quartile and Q3 be the upper quartile of the data set. Find Q1 and Q3 for the
data set.
Q1 =
Q3 =
(b)
Find the interquartile range (IQR) of the data set.
IQR
(c)
=
Calculate a lower boundary using
(Note that
1.5·IQR means 1.5
Q1 − 1.5·IQR. Calculate an upper boundary using Q3 + 1.5·IQR.
times the IQR.)
Lower boundary:
Upper boundary:
(d)
Any values less than the lower boundary or greater than the upper boundary are considered
outliers. Identify all the outliers of the data set. If there is more than one outlier, separate them
with commas. If there are no outliers, write "None".
Outliers:
Question 5 of 17
Assignment - Measures of Position and Transformation #1
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The noon temperatures (in Fahrenheit) for two cities were recorded over a given month.
The box-and-whisker plots below (sometimes called boxplots) summarize the noon temperatures for
each city.
Use the box-and-whisker plots to answer the questions.
City A
City B
55
60
65
70
75
80
85
Noon temperature in Fahrenheit
95
City A
City B
both had the same median
Which city had a larger median noon temperature?
Which city had more noon temperatures above
90
81 °F ?
City A
City B
both had the same number
City A
Which city had noon temperatures with a larger interquartile range (IQR)? City B
both had the same IQR
City A
City B
both had the highest
Which city had the highest noon temperature?
Question 6 of 17
The following are distances (in miles) traveled to the workplace by
16 employees of a certain hospital.
10, 18, 15, 14, 40, 31, 9, 20, 36, 2, 16, 14, 32, 34, 22, 9
Find
30
th
and
th
75
percentiles for these distances.
Question 7 of 17
Assignment - Measures of Position and Transformation #1
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The serum cholesterol levels (in
mg
) of 20 individuals are
dL
247, 198, 201, 191, 196, 242, 254, 220, 208, 206, 259, 232, 252, 218, 240, 257, 235,
215, 237, 244
Find
10
th
and
th
75
percentiles for these cholesterol levels.
Question 8 of 17
The following are the P/E ratios (price of stock divided by projected earnings per share) for
18 banks.
23, 22, 34, 19, 21, 43, 38, 50, 18, 15, 22, 22, 31, 14, 22, 18, 18, 22
Find
40
th
and
th
75
percentiles for these ratios.
Question 9 of 17
A national chain of department stores ranks its
sales. Kala's sales are at the
th
27
750,000
salespeople by the monetary value of their
percentile. Boris's sales are at the
th
64
percentile.
(a) Which of the following must be true about Kala's sales?
About
27% of the salespeople had sales lower in value than Kala.
The value of Kala's sales were about
27% of the chain's total.
The value of Kala's sales was in the top half of all of the salespeople.
Kala sold
$2700 in merchandise.
(b) Which of the following must be true about Kala's and Boris's sales?
Both Kala and Boris had sales higher in value than the median.
Both Kala and Boris had sales lower in value than the median.
Boris's sales were higher in value than Kala's sales.
Kala's sales were higher in value than Boris's sales.
Question 10 of 17
Assignment - Measures of Position and Transformation #1
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Government agencies keep data about the income distribution of the population. The Cox family and
Gonzalez family live in a county with
th
9000 families. The Cox family's income is at the 66
The Gonzalez family's income is at the
nd
32
percentile.
percentile.
(a) Which of the following must be true about the Cox family's income?
The Cox family earns more than about
About
34% of families in their county.
34% of the families in their county earn more than the Cox family.
The Cox family earns about
66% of the highest income in their county.
The Cox family earns about
34% of the highest income in their county.
(b) Which of the following must be true about the Cox family's and the Gonzalez family's
incomes?
The Cox family earns more than the Gonzalez family.
Both the Cox family and the Gonzalez family earn more than the median income.
The Cox family earns
$34,000
more than the Gonzalez family.
The Cox family and the Gonzalez family both have incomes in the bottom half of
incomes in their county.
Question 11 of 17
Yolanda and her family are relocating to Los Angeles. They purchased a home they really like, which
cost
$756,000. The mean home price in the area is $735,000
with a standard deviation
$18,100.
Find the z-score of the price of Yolanda's home relative to the prices among all the homes in the area.
Round your answer to two decimal places.
z=
______
z=
Question 12 of 17
Assignment - Measures of Position and Transformation #1
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Susan runs a large animal shelter. The Smith family adopted a puppy named Bogie from the shelter.
44 days. At Susan's shelter, the length of stay
for puppies has a mean of 61 days and a standard deviation of 9 days.
When Bogie was adopted, he had been at the shelter for
(a)
Find the z-score of Bogie's length of stay at the shelter relative to the the lengths of stay for all
the puppies at the shelter. Round your answer to two decimal places.
z=
(b)
____
Fill in the blanks to interpret the z-score of Bogie's length of stay at the shelter. Make sure to
express your answer in terms of a positive number of standard deviations.
Bogie's length of stay was ____ standard deviations { above | below } the mean
length of stay for all puppies at the shelter.
Question 13 of 17
United County Health and Summertime Sports Center are two local youth basketball leagues. Last
season, the total points scored per player in United County Health had a population mean of
342 points
67 points, and the total points scored per player in Summertime Sports
Center had a population mean of 429 points and a standard deviation of 53 points. For each league, the
and a standard deviation of
distribution of total points scored last season per player was clearly bell-shaped.
Last season, Ann scored a total of 488 points in United County Health and Rita scored a total of
points in Summertime Sports Center.
574
(a) Find the z-scores of Ann's total points scored last season as a player in United County Health and
Rita's total points scored last season as a player in Summertime Sports Center. Round your answers
to two decimal places.
z-score of Ann's total points scored last season: _____
z-score of Rita's total points scored last season: _____
(b) Relative to her population, who was the lower scorer?
Choose the best answer based on the z-scores of the two players.
Ann
Rita
It is unclear who was the lower scorer relative to her population
Question 14 of 17
Assignment - Measures of Position and Transformation #1
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Kira and her family are relocating to Los Angeles and have found a great area in which to live. The
mean price among the homes in the area is
purchased a home for
(a)
$737,000
with a standard deviation of
$18,050. They
$785,000.
Find the z-score of the price of Kira's home relative to the prices among the homes in the area.
Round your answer to two decimal places.
z=
(b)
____
Fill in the blanks to interpret the z-score of the price of Kira's home. Make sure to express your
answer in terms of a positive number of standard deviations.
Kira's home price was ____ standard deviations { above | below } the mean price
among the homes in the area.
Question 15 of 17
A psychologist performed an experiment on participants who used a computer program designed by the
psychologist to assess spatial reasoning. The longer a participant used the computer program, the more
data the psychologist received from the participant.
To entice participants to spend time using the computer program, the psychologist paid each participant
$4.95
for each hour the participant used the computer program in addition to
the experiment. Thus, a participant who used the computer program for
4.95x + 10.75
$10.75
for taking part in
x hours was paid a total of
dollars.
The mean time spent on the computer program by the participants was
deviation of the times was
33 hours, and the standard
8 hours.
(a) What was the mean (in dollars) of the payments to the participants? Do not round your response.
(b) What was the standard deviation (in dollars) of the payments to the participants? Do not round your
response.
Question 16 of 17
Students in a large college class took an exam and did poorly. The mean of the scores for the class was
53 (out of 100), and the standard deviation was 10.
The professor felt that the test may have been too difficult and decided to adjust the scores. She
multiplied each test score by 1.2 and then added 6 to get the adjusted score. In other words, to obtain
the adjusted score
y from the original score x, she used the transformation y = 1.2x + 6.
(a) What is the mean of the adjusted test scores? Do not round your response.
(b) What is the standard deviation of the adjusted test scores? Do not round your response.
Assignment - Measures of Position and Transformation #1
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Question 17 of 17
In experiments in which human reaction times are measured, the times often are recorded in
1/1000 of a second, so the transformation for converting a value m in
milliseconds to a value s in seconds is s = 0.001m.
milliseconds. One millisecond is
In one particular experiment, the reaction times were recorded in milliseconds. Suppose that the mean
of these reaction times was 804 milliseconds and the standard deviation of the reaction times was 158
milliseconds.
(a) What would be the mean of the reaction times measured in seconds? Do not round your response.
(b) What would be the standard deviation of the reaction times measured in seconds? Do not round
your response.
Assignment - Measures of Position and Transformation #1
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Assignment - Measures of Position and Transformation #1
Answers
Class Name : 4th Per - Prob and Stats Honors
Number of Questions: 17
Question 1 of 17
Using Method 1
Using Method 2
Five-number summary
Five-number summary
Minimum:
9
Minimum:
9
Lower quartile:
22
Lower quartile:
22
Median:
28.5
Median:
28.5
Upper quartile:
39
Upper quartile:
39
Maximum:
44
Maximum:
44
Interquartile range:
17
Interquartile range:
17
Question 2 of 17
25
30
35
40
45
50
55
Percentage encountering anti-smoking ad
Question 3 of 17
Assignment - Measures of Position and Transformation #1
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(a) What is the median score?
79
(b) What is the lowest score?
72
(c) What is the first quartile (Q1) of the scores?
75
Question 4 of 17
(a)
Let
Q1 be the lower quartile and Q3 be the upper quartile of the data set. Find Q1 and Q3 for the
data set.
Q1 = 55
Q3 = 62
(b)
Find the interquartile range (IQR) of the data set.
IQR
(c)
=7
Calculate a lower boundary using
(Note that
1.5·IQR means 1.5
Q1 − 1.5·IQR. Calculate an upper boundary using Q3 + 1.5·IQR.
times the IQR.)
44.5
Upper boundary: 72.5
Lower boundary:
(d)
Any values less than the lower boundary or greater than the upper boundary are considered
outliers. Identify all the outliers of the data set. If there is more than one outlier, separate them
with commas. If there are no outliers, click "None".
Outliers: None
Question 5 of 17
Assignment - Measures of Position and Transformation #1
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Which city had a larger median noon temperature?
Which city had more noon temperatures above
City B
81 °F ?
Both had the same number
Which city had noon temperatures with a larger interquartile range (IQR)? City A
Which city had the highest noon temperature?
City B
Question 6 of 17
th
(a)
The
30
(b)
The
75
th
percentile:
14 miles
percentile:
31.75
miles
Question 7 of 17
(a)
(b)
mg
dL
mg
th
The 75 percentile: 246.25
dL
The
th
10
percentile:
196.2
Question 8 of 17
th
(a)
The
40
(b)
The
75
th
percentile:
21.6
percentile:
31.75
Question 9 of 17
(a) Which of the following must be true about Kala's sales?
About
27% of the salespeople had sales lower in value than Kala.
The value of Kala's sales were about
27% of the chain's total.
The value of Kala's sales was in the top half of all of the salespeople.
Kala sold
$2700 in merchandise.
(b) Which of the following must be true about Kala's and Boris's sales?
Both Kala and Boris had sales higher in value than the median.
Both Kala and Boris had sales lower in value than the median.
Boris's sales were higher in value than Kala's sales.
Kala's sales were higher in value than Boris's sales.
Question 10 of 17
Assignment - Measures of Position and Transformation #1
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(a) Which of the following must be true about the Cox family's income?
The Cox family earns more than about
About
34% of families in their county.
34% of the families in their county earn more than the Cox family.
The Cox family earns about
66% of the highest income in their county.
The Cox family earns about
34% of the highest income in their county.
(b) Which of the following must be true about the Cox family's and the Gonzalez family's
incomes?
The Cox family earns more than the Gonzalez family.
Both the Cox family and the Gonzalez family earn more than the median income.
The Cox family earns
$34,000
more than the Gonzalez family.
The Cox family and the Gonzalez family both have incomes in the bottom half of
incomes in their county.
Question 11 of 17
z = 1.16
Question 12 of 17
(a)
Find the z-score of Bogie's length of stay at the shelter relative to the the lengths of stay for all the
puppies at the shelter. Round your answer to two decimal places.
z = − 1.89
(b)
Fill in the blanks to interpret the z-score of Bogie's length of stay at the shelter. Make sure to
express your answer in terms of a positive number of standard deviations.
Bogie's length of stay was
1.89
standard deviations below
▼ the mean length
of stay for all puppies at the shelter.
Question 13 of 17
Assignment - Measures of Position and Transformation #1
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(a) Find the z-scores of Ann's total points scored last season as a player in United County Health and
Rita's total points scored last season as a player in Summertime Sports Center. Round your answers
to two decimal places.
z-score of Ann's total points scored last season: 2.18
z-score of Rita's total points scored last season: 2.74
(b) Relative to her population, who was the lower scorer?
Ann
Rita
It is unclear who was the lower scorer relative to her population
Question 14 of 17
(a)
Find the z-score of the price of Kira's home relative to the prices among the homes in the area.
Round your answer to two decimal places.
z = 2.66
(b)
Fill in the blanks to interpret the z-score of the price of Kira's home. Make sure to express your
answer in terms of a positive number of standard deviations.
Kira's home price was
2.66
standard deviations above
▼ the mean price
among the homes in the area.
Question 15 of 17
What was the mean (in dollars) of the payments to the participants? Do not round your response.
174.10
What was the standard deviation (in dollars) of the payments to the participants? Do not round your
response.
39.60
Question 16 of 17
What is the mean of the adjusted test scores? Do not round your response.
69.6
What is the standard deviation of the adjusted test scores? Do not round your response.
12.0
Question 17 of 17
Assignment - Measures of Position and Transformation #1
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What would be the mean of the reaction times measured in seconds? Do not round your response.
0.804
What would be the standard deviation of the reaction times measured in seconds? Do not round your
response.
0.158
Assignment - Measures of Position and Transformation #1
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