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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