Chapter 1
1–4 You’re
interested in knowing what percent of all households in a large city have a
single woman as the head of the household. To estimate this percentage, you
conduct a survey with 200 households and determine how many of these 200 are
headed by a single woman.
1. In
this example, what is the population?
Answer: all households in the city
A population is the entire group you’re interested in
studying. The goal here is to estimate what percent of all households in a
large city have a single woman as the head of the household. The population is
all households, and the variable is whether a single woman runs the household.
2. In
this example, what is the sample?
Answer: the 200 households selected
The sample is a subset drawn from the entire
population interested for in studying. So in this example, the subset is the
200 households selected out of all the households
3. In
the city. In this example, what is the parameter?
Answer: the
percent of households headed by single women in the city
A parameter is some characteristic of the population.
Because studying a population directly isn’t usually possible, parameters are
usually estimated by using statistics (numbers calculated from sample data).
4. In
this example, what is the statistic?
Answer: the
percent of households headed by single women among the 200 selected households
The statistic is a number describing some
characteristic that you calculate from your sample data; the statistic is used
to estimate the parameter (the same characteristic in the population).
5–6 Answer the
problems about quantitative and Categorical variables.
5. D. a person’s height, recorded in inches
Quantitative variables are measured and expressed
numerically, have numerical meanings, and can be used in calculations. Even
though postcodes are written in numbers, the numbers are just easy labels and
have no numerical meaning.
6. E. Electives (B) and (C) (college majors; high school
graduates or not)
Categorical variables do not have numerical or
quantitative meaning but are simple Describe the quality or characteristics of
something. Majors of courses (such as English or English Mathematics) and high
school graduates (yes or no) both describe non-numeric Quality. The numbers
used in categorical or qualitative data refer to quality rather than a measurement
or quantity. For example, you can assign number 1 to people who are married and
number 2 for people who are not married. The figures themselves have no meaning
- that is, you will not add numbers together.
7. E. All of these choices are correct.
Bias is systematic favouritism in data. You want to
get data that represents all customers in the store, no matter what day or hour
it doesn't even matter. This sample was not taken randomly - everyone who
walked in was counted.
8. E. Choices (C) and (D) (the gender of each shopper who
comes in during the time period; the number of men entering the store during
the time period)
A variable is
a characteristic or measurement on which data is collected and whose result can
change from one individual to the next. That means gender is a variable, and
the number of men entering the store is also a variable. The day you collect
data and the store you observe are just part of the design of your study and
were determined beforehand.
9. In this study, gender is a categorical variable, and number of shoppers is a quantitative variable.
10. D.
Choices (A) and (C) (a bar graph; a pie chart)
Gender is a
categorical variable, so both bar graphs and pie charts are appropriate to
display the proportion of males versus females among the shoppers. You could
use a time plot only if you knew how many males and how many females were in
the store at each individual time period.
11. How would you calculate the mean
number of shoppers per hour?
Answer: Add
together the total shoppers from each observer and divide this total by 3.
The mean
number of shoppers per hour is calculated by dividing the total number of
shoppers (found by adding together the total from each observer) and dividing
by the number of hours
12–17 Answer the problems about different
statistics and data analysis terms
12. E.
Choices (A) and (C) (3, 3, 3, 3, 3; 1, 2, 3, 4, 5)
To find the median, put the data in order from
lowest to highest, and find the value in the middle. It doesn’t matter how many
times a number is repeated. In this case, the data sets 3, 3, 3, 3, 3 and 1, 2,
3, 4, 5 each have a median of 3.
13. Susan scores at the 90th percentile on
a math exam. What does this mean?
Answer:
It means that 90% of students who took the exam had scores less than or equal
to Susan’s.
A percentile
shows the relative standing of a score in a population by identifying the
percent of values below that score. Susan scored in the 90th percentile, so 90%
of the students’ scores are less than or equal to Susan’s.
14. E.
all of the above
All of the
choices are correct. A distribution is basically a list of all possible values
of the variable and how often they occur. In a sentence, you can say, “60% of
the 100 people surveyed said they like chocolate, and 40% said they
don’t” — this sentence gives the distribution. You can also make a
table with rows labeled “Like chocolate” and “Don’t like chocolate” and show
the percents, or you can use a pie chart or a bar graph to visually describe
the distribution.
15. Suppose
that the results of an exam tell you your z-score is 0.70. What does this tell
you about how well you did on the exam?
Answer:
Your score is 0.70 standard deviations above the mean.
A z-score
tells you how many standard deviations a data value is below or above the mean.
If your z-score is 0.70, your exam score is 0.70 standard deviations above the
mean. It doesn’t tell you your actual score or how many students scored above
or below you, but it does tell you where a data value stands, compared to the
average exam score
16. A
national poll reports that 65% of Americans sampled approve of the president,
with a margin of error of 6 percentage points. What does this mean?
Answer:
It means that it’s
likely that between 59% and 71% of all Americans approve of the president.
The margin of
error tells you how much your sample results are likely to change from sample
to sample. It’s measured as “plus or minus a certain amount.” In this case, the
margin of error of 6% tells you that the result from this sample (65% approving
of the president) could change by as much as 6% on either side. Therefore, in
using the sample results to draw conclusions about the whole population, the
best you can say is, “Based on the data, the percentage of all Americans who
approve of the president is likely between 59% (65% – 6%) and 71% (65% + 6%).”
17. If you want to estimate the percentage of all
Americans who plan to vacation for two weeks or more this summer, what
statistical technique should you use to find a range of plausible values for
the true percentage?
Answer:
a confidence interval
You use a
confidence interval when you want to estimate a population parameter
(a number describing the population) when you have no prior information
about it. In a confidence interval, you take a sample, calculate a statistic,
and add/subtract a margin of error to come up with your estimate.
18–19 You read a report that 60% of
high-school graduates participated in sports during their high school years
18. You believe that the percentage of high
school graduates who played sports is higher than what was reported. What type
of statistical technique do you use to see whether you’re right?
Answer:
a hypothesis test
You use a
hypothesis test when someone reports or claims that a population parameter
(such as the population mean) is equal to a certain value and you want to challenge
that claim. Here, the claim is that the percentage of all high-school graduates
who participated in sports is equal to 60%. You think it’s higher than that, so
you’re challenging that claim.
19. E.
p = 0.001
A p-value measures how
strong your evidence is against the other person’s reported value. A small
p-value means your evidence is strong against them; a large p-value says your
evidence is weak against them. In this case, the smallest p-value is 0.001,
which in any statistician’s book is deemed highly significant, meaning your
data and test results show strong evidence against the report. 20.
20. C.
1, 1, 4, 4
The standard deviation measures how
much variability (diversity) is in the data set, compared to the mean. If all
the data values are the same, the standard deviation is 0. To increase the
standard deviation, move the values farther and farther away from the mean. The
choice that moves them the farthest from the mean here is 1, 1, 4, 4.
Chapter
2
21. . To the nearest tenth, what is the
mean of the following data set? 14, 14, 15, 16, 28, 28, 32, 35, 37, 38
Answer:
x
= 14 + 14 + 15 + 16 + 28 + 28 + 32 + 35 + 37 + 38 = 257
n
= 10.
22. To the nearest tenth, what is the mean
of the following data set? 15, 25, 35, 45, 50, 60,70, 72, 100
Answer:
x
= 15 + 25 + 35 + 45 + 50 + 60 + 70 + 72 + 100 = 472
n
= 9.
23. To the nearest tenth, what is the mean
of the following data set? 0.8, 1.8, 2.3, 4.5, 4.8, 16.1, 22.3
Answer:
x = 0.8 + 1.8 + 2.3 + 4.5 + 4.8 + 16.1
+ 22.3 = 52.6
n = 7.
24. To the nearest thousandth, what is the mean of
the following data set? 0.003, 0.045, 0.58,0.687, 1.25, 10.38, 11.252, 12.001
Answer:
x = 0.003 + 0.045 + 0.58 + 0.687 +
1.25 + 10.38 + 11.252 + 12.001 = 36.198
n = 8
25. To the nearest tenth, what is the median of
the following data set? 6, 12, 22, 18, 16,4, 20, 5, 15
Answer:
X=
4, 5, 6, 12, 15, 16, 18, 20, 22
Median
= 15
26. To the nearest tenth, what is the
median of the following data set? 18, 21, 17, 18, 16,15.5, 12, 17, 10, 21, 17
Answer:
X= 10, 12, 15.5, 16, 17, 17, 17, 18, 18,
21, 21
Median = 17
27. To the nearest tenth, what is the median of
the following data set? 14, 2, 21, 7, 30, 10, 1, 15, 6, 8
Answer:
X= 1, 2, 6, 7, 8, 10, 14, 15, 21, 30
28. To the nearest hundredth, what is the
median of the following data set? 25.2, 0.25,8.2, 1.22, 0.001, 0.1, 6.85, 13.2
Answer:
X = 0.001, 0.1, 0.25, 1.22, 6.85, 8.2, 13.2, 25.2
49–56 Use the empirical rule to solve the
following problems.
49. According
to the empirical rule (or the 68-95- 99.7 rule), if a population has a normal
distribution, approximately what percentage of values is within one standard
deviation of the mean?
Answer:
approximately 68%
The empirical
rule states that in a normal (bell-shaped) distribution, approximately 68% of
values are within one standard deviation of the mean.
50. According
to the empirical rule (or the 68-95- 99.7 rule), if a population has a normal
distribution, approximately what percentage of values is within two standard
deviations of the mean?
Answer: about 95%
The empirical
rule states that in a normal (bell-shaped) distribution, approximately 95% of
values are within two standard deviations of the mean.
51. If the average age of retirement for the
entire population in a country is 64 years and the distribution is normal with
a standard deviation of 3.5 years, what is the approximate age range in which
95% of people retire?
Answer:
about 57 to 71 years
The empirical
rule states that in a normal distribution, 95% of values are within two
standard deviations of the mean. “Within two standard deviations” means two
standard deviations below the mean and two standard deviations above the mean.
In this case, the mean is 64 years, and the standard deviation is 3.5 years. So
two standard deviations is (3.5)(2) = 7 years. To find the lower end of the
range, subtract two standard deviations from the mean: 64 – 7 years = 57
years. And then to find the upper end of the range, add two standard deviations
to the mean: 64 + 7 years = 71 years. So about 95% of people who retire do so
between the ages of about 57 to 71 years.
52. Last
year’s graduates from an engineering college, who entered jobs as engineers,
had a mean first-year income of $48,000 with a standard deviation of $7,000.
The distribution of salary levels is normal. What is the approximate percentage
of first-year engineers that made more than $55,000?
Answer:
about 16%
The empirical
rule states that approximately 68% of values are within one standard deviation
of the mean. “Within one standard deviation” means one standard deviation below
the mean and one standard deviation above the mean. In this case, the mean is
$48,000, so about 50% of the engineers made less than $48,000. In a normal
distribution, half of the values are above the mean and half are below the
mean. The standard deviation is $7,000.
To find the lower end of the range
within one standard deviation of the mean, subtract the standard deviation from
the mean: $48,000 – $7,000 = $41,000;
to find the upper end of the range, add the standard deviation to the mean: $48,000 + $7,000 = $55,000.
Because the normal distribution is
symmetrical, 34% of the values will be between $41,000 and $48,000, and 34%
will be between $48,000 and $55,000. Therefore, 50% + 34% = 84% of the data is $55,000 and below, which leaves 16%
of the data above $55,000.
53. What is a
necessary condition for using the empirical rule (or 68-95-99.7 rule)?
Answer: if a population has a normal
distribution
You can use the empirical rule only if the
distribution of the population is normal. Note that the rule says that if the
distribution is normal, then approximately 68% of the values lie within one
standard deviation of the mean, not the other way around. Many distributions
have 68% of the values within one standard deviation of the mean that don’t
look like a normal distribution.
54. What
measures of data need to be known to use the empirical (68-95-99.7) rule?
Answer:
the mean and the standard deviation of the population
The empirical rule describes the distribution
of the data in a population in terms of the mean and the standard deviation.
For example, the first part of the empirical rule says that about 68% of the
values lie within one standard deviation of the mean, so all you need to know
is the mean and the standard deviation to use the rule.
55. The
quality control specialists of a microscope manufacturing company test the lens
for every microscope to make sure the dimensions are correct. In one month, 600
lenses are tested. The mean thickness is 2 millimeters. The standard deviation
is 0.000025 millimeters. The distribution is normal. The company rejects any
lens that is more than two standard deviations from the mean. Approximately how
many lenses out of the 600 would be rejected?
Answer:
30
If you assume that the 600 lenses tested come
from a population with a normal distribution (which they do), you can apply the
empirical rule (also known as the 68-95-99.7 rule). Using the empirical rule,
approximately 95% of the data lies within two standard deviations of the mean,
and 5% of the data lies outside this range. Because the lenses that are more
than two standard deviations from the mean are rejected, you can expect about
5% of the 600 lenses, or (0.05)(600) = 30 lenses to be rejected.
56. Biologists
gather data on a sample of fish in a large lake. They capture, measure the
length of, and release 1,000 fish. They find that the standard deviation is 5
centimeters, and the mean is 25 centimeters. They also notice that the shape of
the distribution (according to a histogram) is very much skewed to the left
(which means that some fish are smaller than most of the others). Approximately
what percentage of fish in the lake is likely to have a length within one
standard deviation of the mean?
Answer:
cannot be determined with the information given
You could use the empirical rule (also known
as the 68-95-99.7 rule) if the shape of the distribution of fish lengths was
normal; however, this distribution is said to be “very much skewed left,” so
you can’t use this rule. With the information given, you can’t answer the
question
57–64 Solve the following problems about
percentiles.
57. What
statistic reports the relative standing of a value in a set of data?
Answer:
percentile
A percentile
splits the data into two parts, the percentage below the value and the
percentage above the value. In other words, a percentile measures where an individual
data value stands compared to the rest of the data values.
58. What is
the statistical name for the 50th percentile?
Answer:
median
The 50th percentile is the value where 50% of
the data fall below it and 50% fall above it. This is the same as the
definition of the median.
59. Your score
on a test is at the 85th percentile. What does this mean?
Answer:
It means that 15% of the scores were better than your score.
Percentile is
the relative standing in a set of data from the lowest values to highest
values. If your score is in the 85th percentile, it means that 85% of the
scores are below your score and 15% are above your score.
60. Suppose
that in a class of 60 students, the final exam scores have an approximately
normal distribution, with a mean of 70 points and a standard deviation of 5
points. Bob’s score places him in the 90th percentile among students on this
exam. What must be true about Bob’s score?
Answer:
Bob’s score is above 70.
A score in the
90th percentile means that 90% of the scores were lower. With 60 scores and an
approximately normal distribution, the 90th percentile will certainly be above
the mean, here given as 70.
61. On a
multiple-choice test, your actual score was 82%, which was reported to be at
the 70th percentile. What is the meaning of your test results?
Answer:
It means that 30% of the students scored above you and that you correctly
answered 82% of the test questions.
The 70th
percentile means that 70% of the scores were below your score, and 30% were
above your score. Your actual score was 82%, which means that you answered 82%
of the test questions correctly.
62. Seven
students got the following exam scores (percent correct) on a science exam: 0%,
40%, 50%, 65%, 75%, 90%, 100%. Which of these exam scores is at the 50th
percentile?
Answer:
65%
The 50th
percentile doesn’t mean a score of 50%; it’s the median (or middle number) of
the data set. The middle number is 65%, so that is the 50th percentile.
63. Students
scored the following grades on a statistics test: 80, 80, 82, 84, 85, 86, 88,
90, 91, 92, 92, 94, 96, 98, 100. Calculate the score that represents the 80th
percentile.
Answer:
95
1. Put all the numbers in the data set in
order from smallest to largest: 80, 80,
82, 84, 85, 86, 88, 90, 91, 92, 92, 94, 96, 98, 100
2.
Multiply
k percent by the total number of values, n:
(0.80)(15) = 12
3.
Because
your result in Step 2 is a whole number, count the numbers in the data
set from left to right until you reach the number you found in
Step 2 (in this case, the 12th number). The kth percentile is the
average of that corresponding value in the data set and the
value that directly follows it. Find the average of the 12th and 13th numbers
in the data set:
64. Some of
the students in a class are comparing their grades on a recent test. Mary says
she almost scored in the 95th percentile. Lisa says she scored at the 84th
percentile. Jose says he scored at the 88th percentile. Paul says he almost
scored in the 70th percentile. Bill says he scored at the 95th percentile. Rank
the five students from highest to lowest in their grades.
Answer:
Bill, Mary, Jose, Lisa, then Paul
If your score
is at the kth percentile, that means k percent of the students scored less than
you did, and the rest scored better than you did. For example, someone scoring
at the 95th percentile knows that 95% of the other students scored lower than
he did, and 5% scored higher.
When talking
about exam scores, the person that scores at the highest percentile scored
better than everyone else on the list. So in ranking from highest to lowest in
terms of where their grades stand compared to each other, you have Bill first,
followed by Mary, then Jose, then Lisa, and then Paul.
65. B. the median
The median of
a data set is the middle value after you’ve put the data in order from smallest
to largest (or the average of the two middle values if your data set contains
an even number of values). Because the median concerns only the very middle of
the data set, adding an outlier won’t affect its value much (if any). It adds
only one more value to one end or the other of the sorted data set.
66. E. None of the above.
It’s strange but true that all the scenarios
are possible. You can use one data set as an example where all four scenarios
occur at the same time: 5, 5, 5, 5, 5, 5, 5. In this case, the minimum and
maximum are both 5, and the median (middle value) is 5. The median cuts the
data set in half, creating an upper half and a lower half of the data set. To
find the 1st quartile, take the median of the lower half of the data set,
which gives you 5 in this case; to find the 3rd quartile, take the median of
the upper half of the data set (also 5). The range is the distance from the
minimum to the maximum, which is 5 – 5 = 0. The IQR is the distance from the 1st
to the 3rd quartile, which is 5 – 5 = 0. Hence, the range and IQR are the same.
67. Test
scores for an English class are recorded as follows: 72, 74, 75, 77, 79, 82,
83, 87, 88, 90, 91, 91, 91, 92, 96, 97, 97, 98, 100. Find the 1st quartile,
median, and 3rd quartile for the data set.
Answer
: 1st quartile = 79, median = 90,
3rd quartile = 96 The 1st quartile is
the 25th percentile, the median is the 50th percentile, and the 3rd quartile is
the 75th percentile.
To find the values for these numbers,
use the procedure for calculating a percentile. To calculate the kth
percentile (where k is any number between 1 and 100), follow these steps:
1.
Put
all the numbers in the data set in order from smallest to largest: 72, 74, 75,
77, 79, 82, 83, 87, 88, 90, 91, 91, 91, 92, 96, 97, 97, 98, 100
2.
Multiply k percent times the total number of
values, n. For the 1st quartile (or 25%): (0.25)(19) = 4.75. For the median (or
50%): (0.50)(19) = 9.5. For the 3rd quartile (or 75%): (0.75)(19) = 14.25
3.
Because
the results in Step 2 aren’t whole numbers, round up to the nearest
whole number, and then count the numbers in the data set from left to
right (from the smallest to the largest number) until you reach
the value of the rounded number. The corresponding value in the
data set is the kth percentile.
For
the 1st quartile, round 4.75 up to 5 and then find the fifth number in the
data set: 79.
For the median, round 9.5 up to 10 and then find the
tenth number in the data set: 90.
For
the 3rd quartile, round 14.25 up to 15 and then find the 15th number in the
data set: 96.
68. The
five-number summary can’t be found.
The
five-number summary of a data set includes the minimum value, the 1st quartile,
the median, the 3rd quartile, and the maximum value. You’re not given the
minimum value or the maximum value here, so you can’t fill out the five-number
summary.
Note that even
though you’re given the range, which is the distance between the maximum and
minimum values, you can’t determine the actual values of the minimum and
maximum.
69. The median
can’t be greater in value than the 3rd quartile.
The five
numbers in the five-number summary are the minimum (smallest) number in the
data set, the 25th percentile (also known as the 1st quartile, or Q1), the
median (50th percentile), the 75th percentile (also known as the 3rd quartile,
or Q3), and the maximum (largest) number in the data set.
Because the
median is at the 50th percentile, its value must be between the value of
the 1st and 3rd quartiles, inclusive. In this case, the 1st quartile is
50, and the 3rd quartile is 80, so a median of 85 isn’t possible.
Chapter 3
88–94 The following bar chart represents
the post-graduation plans of the graduating seniors from one high school.
Assume that every student chose one of these five options. (Note: A gap year
means that the student is taking a year off before deciding what to do.)
88. What is
the most common post-graduation plan for these seniors?
Answer:
Attend a university.
University is the tallest bar in the graph and
therefore represents the greatest number of students of any category
89. What is
the least common post-graduation plan for these seniors? 90. Assuming that each
student has chosen only one of the five possibilities, about how many students
plan to either ta
Answer: Go
into the military.
Military is
the shortest bar in the graph and therefore represents the fewest number of
students.
90. Assuming
that each student has chosen only one of the five possibilities, about how many
students plan to either take a gap year or attend a university?
Answer:
140
Judging by the
height of the bars, about 120 students plan to attend a university, and about
20 plan to take a gap year. So 120 + 20
= 140 students
91. How many
total students are represented in this chart?
Answer:
322
120 + 82 + 18 + 82 + 20 = 322
92. What
percentage of the graduating class is planning on attending a community
college?
Answer:
25%
You can find
the number of students in each category from the height of the bars. The total
number of students is 322 (120 + 82 + 18
+ 82 + 20 = 322). The number going to a community college is 82. To find
the percentage of students going to a community college, divide the number
of students in that category by the total number of students: 82/322 = 0.2546, or about 25%.
93. What
percentage of the graduating class is not planning to attend a university?
Answer:
63%
Judging from
the height of the bars, there are 322 students total (120 + 82 + 18 + 82 + 20 = 322), and 120 plan to attend a
university. To find the percentage of students not planning to attend a
university, subtract the number that do plan to attend from the total number of
students (322 – 120 = 202), and then
divide by the total: 202/322 = 0.627,
or about 63%.
94. This bar
chart displays the same information but is more difficult to interpret. Why is
this the case?
Answer:
histogram
Because the
data is continuous with many possible values, a histogram would be the best
choice for displaying this type of data.
106–112 The following histogram represents
the reported income from a sample of 110 U.S. adults.
106. How would
you describe the shape of this distribution?
Answer: right-skewed
The data is
right-skewed because it has a large number of values in the lower income range
and a long tail extending to the right, representing a few cases with high
incomes.
107. What
would be the most appropriate measure of the center for this data?
Answer:
median
The median is
the best measure of the center when the data is highly skewed, and it’s less
affected by extreme values than the mean. Because the mean uses the value of
every number in its calculation, the few high values pull the mean upward,
while the median stays in the middle and is a better representative of the
“center” of the data.
108. Which value will be higher in this
distribution, the mean or the median?
Answer:
The mean will be higher.
In a
right-skewed distribution, the mean will be greater than the median because it
has a few high values compared to the rest, pulling the average up. The median
is just the middle number when the data is ordered, so the few high values
can’t pull up the median.
109. What is
the lowest possible value in this data?
Answer:
0
The lowest
possible value is 0 because the values in the first bar (looking at the x-axis)
go from 0 to 5,000. Note: You can’t tell whether 0 is actually in the data set,
so you know only that the lowest possible value is 0.
110. What is
the highest possible value in this data?
Answer:
85,000
Each bar
represents a range of 5,000 (looking at the x-axis). The lower bound of the
highest bar is 80,000, so its upper bound is 85,000.
111. How many
adults in this sample reported an income less than $10,000?
Answer:
35
The height of a bar represents the number of people in
that range. Each bar covers a range of $5,000 in income, so the first two bars
represent incomes less than $10,000. The first bar has a height of about 11 and
the second has a height of about 24. Together, that’s 35 (11 + 24 = 35).
112. Which bar
contains the median for this data? (Denote the bar by using its left endpoint
and its right endpoint.)
Answer:
$10,000 to $15,000
The sample
includes 110 adults, and if you sort their incomes from lowest to highest, the
median is the number in the middle (between the 55th and 56th numbers). To find
the bar that contains the median, count the heights of the bars until you reach
55 and 56. The third bar contains the median and ranges from $10,000 to
$15,000.
121–125 The following box plot represents
data on the GPA of 500 students at a high school.
121. What is
the range of GPAs in this data?
Answer:
2.5
The range of
data is from 1.5 to 4.0, which is 4.0 – 1.5 = 2.5.
122. What is
the median of the GPAs?
Answer:
3.0
The thick line
within the box indicates the median (or middle number) for the data.
123. What is
the IQR for this data?
Answer:
1.125
The
interquartile range (IQR) is the distance between the 1st and 3rd quartiles
(Q1 and Q3). In this case, IQR = 3.5 – 2.375 = 1.125.
124. What does
the scale of the numerical axis signify in this box plot?
Answer:
the GPA values
The numerical
axis is a scale showing the GPAs of individual students ranging from
1.5 to 4.0.
125. Where is
the mean of this data set?
Answer:
cannot tell
A box plot includes five values: the minimum
value, the 25th percentile (Q1), the median, the 75th percentile (Q3), and the
maximum value. The value of the mean isn’t included on a box plot.
Sumber jawaban
: chapter 18
1,001
Statistics Practice Problems For Dummies® Published by: John Wiley & Sons,
Inc., 111 River Street, Hoboken, NJ 07030-5774, www.wiley.com Copyright © 2014
by John Wiley & Sons, Inc., Hoboken, New Jersey
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