business statistics chapter 2
(3)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.Using the number of hospitals per state listed in the table above, make a stem-and-leaf display for the number of community hospitals per state. (Enter NONE in any unused answer blanks.)Which states have an unusually high number of hospitals? (Select all that apply.)
0-8,1-12569,2-177,3-578,4-127,5-1239,6-168,7-1,8-8,9-0268,10-127,11-3379,12-239,13-336,14-8,15-none,16-2,17-5,18-none,19-3,20-9,21-none,22-7,23-16,42-1,43-none,44-0, Texas California
The following data represent glucose blood levels (mg/100 ml) after a 12-hour fast for a random sample of 70 women (Reference: American Journal of Clinical Nutrition, Vol. 19, pp. 345-351).a) Find the class width.b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Round your relative frequencies to four decimal places.)c) Draw a histogram. d) Draw a relative-frequency histogram.e) Categorize the basic distribution shape.f) Draw an ogive.
a)11, b)check notes, c)check notes, d)check notes,e)mound-shaped symmetrical, f) check notes
(2)The book The Wall Street Journal. Guide to Information Graphics by Dona M. Wong gives strategies for using graphs and charts to display information effectively. One popular graph discussed is the donut pie chart. The donut pie chart is simply a pie chart with the center removed. A recent Harris Poll asked adults about their opinions regarding whether books should be banned from libraries because of social, language, violent, sexual, or religious content. The responses by education level to the question "Do you think that there are any books which should be banned completely?" are shown in the following donut pie charts.a) What feature of Keith's graph makes it difficult to visually compare the responses of those with some college to those shown in the other graphs? How would you change Keith's graph for easier comparison? b) Compare graphs made by Ramon. At which of the two education levels is the "no" response more frequent?
2a)The donut hole in the graph made by Keith is a different size than in the graphs made by Ramon.The graphs do not have data labels showing the percentages.,Add data labels showing the percentages.Make all donuts exactly the same size, with the radius of the holes the same as well. 2b)College graduate
(3)How long did real cowboys live? One answer may be found in the book The Last Cowboys by Connie Brooks (University of New Mexico Press). This delightful book presents a thoughtful sociological study of cowboys in West Texas and Southeastern New Mexico around the year 1890. A sample of 32 cowboys gave the following years of longevity: 58,52,68,86,72,66,97,89,84,91,91,92,66,68,87,86,73,61,70,75,72,73,85,84,90,57,77,76,84,93,58,47 (a) Make a stem-and-leaf display for these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter numbers from smallest to largest separated by spaces. Enter NONE for stems with no values.)b) Consider the following quote from Baron von Richthofen in his Cattle Raising on the Plains of North America: "Cowboys are to be found among the sons of the best families. The truth is probably that most were not a drunken, gambling lot, quick to draw and fire their pistols." Does the data distribution of longevity lend credence to this quote?
3a) 4-7,5-2788,6-16688,7-02233567,8-44456679,9-011237, 3b)Yes, these cowboys certainly lived long lives, as evidenced by the high frequency of leaves for stems 7, 8, and 9 (i.e., 70-, 80-, and 90-year-olds).
(3)The U.S. Open Golf Tournament was played at Congressional Country Club, Bethesda, Maryland, with prizes ranging from $465,000 for first place to $5000. Par for the course is 70. The tournament consists of four rounds played on different days. The scores for each round of the 32 players who placed in the money (more than $17,000) are given. The scores for the first round were as follows.The scores for the fourth round for these players were as follows.a) Make a stem-and-leaf display for the first-round scores. Use two lines per stem. (Enter your answers from smallest to largest separated by spaces. Enter NONE for stems with no leaves.)b) Make a stem-and-leaf display for the fourth-round scores. Use two lines per stem. (Enter your answers from smallest to largest separated by spaces. Enter NONE for stems with no leaves.)(c) Compare the two distributions. How do the highest scores compare? How do the lowest scores compare? (Select all that apply.)
4a) check notes 4b)check notes 4c)In the first round, both the low and high scores were more extreme than in the fourth round. Scores are higher in the first round
(3)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.Make a stem-and-leaf display of the data for the average length of stay in days. (Use the digit(s) to the left of the decimal point as the stem and the digit to the right as the leaf. Enter NONE in any unused answer blanks.)Comment about the general shape of the distribution.
5-235567,6-0246677888899,7-00000011122233334455668,8-457,9-469,10-03,11-1,The distribution is skewed right.
(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?
A time-series graph because the pattern of stock prices over time is more relevant than the frequency of a range of closing prices.
What is the difference between a class boundary and a class limit?
Class boundaries are values halfway between the upper class limit of one class and the lower class limit of the next..Class boundaries are not possible data values.Class limits are possible data values..Class limits specify the span of data values that fall within a class.
(2)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?
Pareto chart, because it shows the items in order of importance to employees
A data set has values ranging from a low of 10 to a high of 50. What's wrong with using the class limits 10-20, 20-30, 30-40, 40-50 for a frequency table?
The classes overlap so that some data values, such as 20, fall within two classes.
The ogives shown are based on U.S. Census data and show the average annual personal income per capita for each of the 50 states. The data are rounded to the nearest thousand dollars.(a) How were the percentages shown in graph (ii) computed? b)How many states have average per capita income less than 37.5 thousand dollars?c) How many states have average per capita income between 42.5 and 52.5 thousand dollars?d) What percentage of the states have average per capita income more than 47.5 thousand dollars?
The percentages in graph (ii) were computed by dividing each of the cumulative frequencies in graph (i) by 50 and then converting those values into percents.,35,5,4
Another display technique that is somewhat similar to a histogram is a dotplot. In a dotplot, the data values are displayed along the horizontal axis. A dot is then plotted over each data value in the data set. For more details, view How to Make a Dotplot. The figure below shows a dotplot generated by Minitab for the number of licensed drivers per 1000 residents by state, including the District of Columbia (Source: U.S. Department of Transportation).a) From the dotplot, how many states have 600 or fewer licensed drivers per 1000 residents?b) About what percentage of the states (out of 51) seem to have close to 800 licensed drivers per 1000 residents? (Round your answer to one decimal place.)c) Consider the intervals 550 to 650, 650 to 750, and 750 to 850 licensed drivers per 1000 residents. In which interval do most of these states fall?
a) 1,b)9.8%c)650-750
What percent of undergraduate enrollment in coed colleges and universities in the United States is male? A random sample of 50 such institutions give the following data.a) Find the class width.b) Make a frequency table showing class limits, class boundaries, midpoints, frequencies, relative frequencies, and cumulative frequencies. (Round your relative frequencies to four decimal places.)c) Draw a histogram. d) Draw a relative-frequency histogram.e) Categorize the basic distribution shape.f) Draw an ogive.
a)11, b)check notes, c)check notes, d)check notes,e)skewed right, f) check notes
(2)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. Bann 18, Blackwater 8, Erne 15, Shannon 28, Barrow 14 a) Make a Pareto chart for these data. b) Make a circle graph for these data.
a)c check notes b) d check notes
How long does it take to finish the 1161-mile Iditarod Dog Sled Race from Anchorage to Nome, Alaska? Finish times (to the nearest hour) for 27 dogsled teams are shown below.Compare the dotplot to a histogram of the data.
a)check notes b)Dotplots show the frequency of individual data values.The raw data can be retrieved from the dotplot, but not the histogram.The dotplot and histogram both show a greater density from 280 to 340.
Certain kinds of tumors tend to recur. The following data represent the lengths of time, in months, for a tumor to recur after chemotherapy (Reference: D.P. Byar, Journal of Urology, Vol. 10, pp. 556-561).a) Make a dotplot for the data above regarding the recurrence of tumors after chemotherapy. Select the appropriate dotplot below.b) Compare the dotplot to a histogram of the data.
a)check notes b)The raw data can be retrieved from the dotplot, but not the histogramDotplots show the frequency of individual data values.
(2)Driving would be more pleasant if we didn't have to put up with the bad habits of other drivers. A newspaper reported the results of a Valvoline Oil Company survey of 500 drivers in which the drivers marked their complaints about other drivers. The top complaints turned out to be tailgating, marked by 23% of the respondents; not using turn signals, marked by 20%; being cut off, marked by 16%; other drivers driving too slowly, marked by 10%; and other drivers being inconsiderate marked by 8%. (a) Make a Pareto chart showing percentage of drivers listing each stated complaint. (b) Could this information as reported be put in a circle graph? Why or why not?
c (b)Since the percentages do not add to 100%, a circle graph cannot be used. If we create an "other" category and assume that all other respondents fit this category, then a circle could be created.
(2)How do college professors spend their time? The National Education Association Almanac of Higher Education gives the following average distribution of professional time allocation: teaching, 49%; research, 18%; professional growth, 5%; community service, 11%; service to the college, 11%; and consulting outside the college, 6%. Make a pie chart showing the allocation of professional time for college professors.
c check notes
(2)The elevation of a lake surface (feet above sea level) varies according to the annual flow of a river that feeds it. A geological survey provided the following data from equally spaced intervals of time over a 15 year period.1 -2817 2-2815 3-2810 4-2812 5-2808 6-2803 7-2798 8-2797 9-2795 10-2797 11 2802 12-2807 13-2811 14-2816 15-2817
c-check notes
(2)It is costly in both time and money to go to college. Does it pay off? According to the Bureau of the Census, the answer is yes. The average annual income (in thousands of dollars) of a household headed by a person with the stated education level is as follows: 24.3 if ninth grade is the highest level achieved, 41.5 for high school graduates, 59.2 for those holding associate degrees, 82.4 for those with bachelor's degrees, 100.4 for those with master's degrees, and 121.6 for those with doctoral degrees. Make a bar graph showing household income for each education level.
d) check notes
