MATH 201

Week 2: Exercises (2.2 – 3.3)

1. A personnel office is gathering data
regarding working conditions. Employees are given a list of five
conditions that they might want to see improved. They are asked to
select the one item that is most critical to them. Which type of
graph, circle graph or Pareto chart, would be the most useful for
displaying the results of the survey? Why?

2. Your friend is thinking about buying
shares of stock in a company. You have been tracking the closing
prices of the stock shares for the past 90 trading days. Which type
of graph for the data, histogram or time-series, would be best to
show your friend? Why?

3. Commercial dredging operations in
ancient rivers occasionally uncover archaeological artifacts of
great importance. One such artifact is Bronze Age spearheads
recovered from ancient rivers in Ireland. A recent study gave the
following information regarding discoveries of ancient bronze
spearheads in Irish rivers.

4. How does average height for boys change
as boys get older? According to Physician’s Handbook, the
average heights at different ages are in the table below.

5. Wetlands offer a diversity of benefits.
They provide a habitat for wildlife, spawning grounds for U.S.
commercial fish, and renewable timber resources. In the
last 200 years, the United States has lost more than half
its wetlands. Environmental Almanac gives the percentage
of wetlands lost in each state in the last 200 years. For
the 30 of the lower 48 states, the percentage loss of
wetlands per state is as follows.

1. The American Medical Association Center
for Health Policy Research included data, by state, on the number
of community hospitals and the average patient stay (in days) in
its publication State Health Care Data: Utilization, Spending, and
Characteristics. The data (by state) are shown in the table.

2. What symbol is
used for the arithmetic mean when it is a sample statistic? What
symbol is used when the arithmetic mean is a population parameter?

Find the mean, median, and mode of the data set.

Find the mean, median, and mode of the data set.

3. Consider a data set with at least three
data values. Suppose the highest value is increased by 10 and the
lowest is decreased by 10.

4. Consider the following types of data
that were obtained from a random sample of 49 credit card accounts.
Identify all the averages (mean, median, or mode) that can be used
to summarize the data. (Select all that apply.)

5. In this problem, we explore the effect
on the mean, median, and mode of adding the same number to each
data value. Consider the data
set 4, 4, 5, 8, 12.

6. In this problem, we explore the effect
on the mean, median, and mode of multiplying each data value by the
same number. Consider the following data set. 6, 6, 7, 10, 14.

7. How hot does it get in Death Valley? The
following data are taken from a study conducted by the National
Park System, of which Death Valley is a unit. The ground
temperatures (°F) were taken from May to November in the vicinity
of Furnace Creek. Compute the mean, median, and mode for these
ground temperatures. (Enter your answers to one decimal place.)

8. How old are professional football
players? The 11th Edition of The Pro Football
Encyclopedia gave the following information. Random sample of
pro football player ages in years:

9. In your biology class, your final grade
is based on several things: a lab score, scores on two major tests,
and your score on the final exam. There are 100 points available
for each score. However, the lab score is worth 25% of
your total grade, each major test is worth 24%, and the final
exam is worth 27%. Compute the weighted average for the
following scores: 86 on the lab, 93 on the
first major test, 65 on the second major test,
and 66 on the final exam.

10. Which average – mean, median, or
mode – is associated with the standard deviation?Mean

11. What is the relationship between
the variance and the standard deviation for a sample data set?The
standard deviation is the square root of the variance.

When computing the standard deviation, does it matter whether
the data are sample data or data comprising the entire population?
Explain.

What symbol is used for the standard deviation when it is a
sample statistic? What symbol is used for the standard deviation
when it is a population parameter?

12. Consider the data set. 2, 5, 7, 8, 9

13. Each of the following data sets has a mean
of x = 10.

14. In this problem, we explore the effect on the standard
deviation of adding the same constant to each data value in a data
set. Consider the following data set.

15. In this problem, we explore the effect on the standard
deviation of multiplying each data value in a data set by the same
constant. Consider the data
set 12, 16, 15, 12, 9.

16. One indicator of an outlier is that an observation is
more than 2.5 standard deviations from the mean. Consider the data
value 80.

17. Angela took a general aptitude test and scored in
the 91st percentile for aptitude in accounting.

18. One standard for admission to Redfield College is that
the student must rank in the upper quartile of his or her
graduating high school class. What is the minimal percentile rank
of a successful applicant?

The town of Butler, Nebraska, decided to give a
teacher-competency exam and defined the passing scores to be those
in the 70th percentile or higher. The raw test scores ranged from 0
to 100. Was a raw score of 82 necessarily a passing score?
Explain.

different final exam. Timothy scored 83 out of 100 and had a
percentile rank in his class of 72. Clayton scored 85 out of 100
but his percentile rank in his class was 70. Who performed better
with respect to the rest of the students in the class, Clayton or
Timothy? Explain your answer.

19. At one hospital there is some concern about the high
turnover of nurses. A survey was done to determine how long (in
months) nurses had been in their current positions. The responses
(in months) of 20 nurses were as follows.

20. What percentage of the general U.S. population have
bachelor’s degrees? The Statistical Abstract of the United
States, 120th Edition, gives the percentage of bachelor’s degrees
by state. For convenience, the data are sorted in increasing order.

21. Some data sets include values so high or so low that they
seem to stand apart from the rest of the data. These data are
called outliers. Outliers may represent data collection
errors, data entry errors, or simply valid but unusual data values.
It is important to identify outliers in the data set and examine
the outliers carefully to determine if they are in error. One way
to detect outliers is to use a box-and-whisker plot. Data values
that fall beyond the limits

22. What percentage of the general U.S. population are
high-school dropouts? The Statistical Abstract of the United
States, 120th Edition, gives the percentage of high-school dropouts
by state. For convenience, the data are sorted in increasing
order.

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