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Chapter 2: Q39E (page 94)
Calculate the mode, mean, and median of the following data:
18 10 15 13 17 15 12 15 18 16 11
Mode = 15.
Mean = 14.54.
Median = 15.
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Question: Hull failures of oil tankers.Owing to several major ocean oil spills by tank vessels, Congress passed the Oil Pollution Act, which requires all tankers to be designed with thicker hulls. Further improvements in the structural design of a tank vessel have been proposed since then, each with the objective of reducing the likelihood of an oil spill and decreasing the amount of outflow in the event of a hull puncture. To aid in this development, Marine Technology (Jan. 1995) reported on the spillage amount (in thousands of metric tons) and cause of puncture for 50 major oil spills from tankers and carriers. [Note: Cause of puncture is classified as either collision (C), fire/explosion (FE), hull failure (HF), or grounding (G).] The data are saved in the accompanying file.
a.Use a graphical method to describe the cause of oil spillage for the 50 tankers. Does the graph suggest that any one cause is more likely to occur than any other? How is this information of value to the design engineers?
b.Find and interpret descriptive statistics for the 50 spillage amounts. Use this information to form an interval that can be used to predict the spillage amount of the next major oil spill.
Performance of stock screeners.Investment companies provide their clients with automated tools鈥攃alled stock screeners鈥攖o help them select a portfolio of stocks to invest in. The American Association of Individual Investors (AAII) provides statistics on stock screeners at its Website, www.aaii.com. The next table lists the annualized percentage return on investment (as compared to the Standard & Poor鈥檚 500 Index) for 13 randomly selected stock screeners. (Note:A negative annualized return reflects a stock portfolio that performed worse than the S&P 500.)
(9.0, -.1, -1.6, 14.6, 16.0, 7.7, 19.9, 9.8, 3.2, 24.8, 17.6, 10.7, 9.1)
a.Compute the mean for the data set. Interpret its value.
b.Compute the median for the data set. Interpret its value.
Thousands of students apply for admission to graduate schools in economics each year with the intention of obtaining a PhD. The Southern Economic Journal (April 2008) published a guide to graduate study in economics by ranking the PhD programs at 129 colleges and universities. Each program was evaluated according to the number of publications published by faculty teaching in the PhD program and by the quality of the publications. Data obtained from the Social Science Citation Index (SSCI) were used to calculate an overall productivity score for each PhD program. The mean and standard deviation of these 129 productivity scores were then used to compute a z-score for each economics program. Harvard University had the highest z-score 1z = 5.082 and, hence, was the top-ranked school; Howard University was ranked last because it had the lowest z-score 1z = -0.812. The data (z-scores) for all 129 economic programs are saved in the data file.
a. Interpret the z-score for Harvard University.
b. Interpret the z-score for Howard University.
c. The authors of the Southern Economic Journal article note that 鈥渙nly 44 of the 129 schools have positive z-scores, indicating that the distribution of overall productivity is skewed to the right.鈥� Do you agree?
Calculate the range, variance, and standard deviation for the following samples:
a.4, 2, 1, 0, 1
b.1, 6, 2, 2, 3, 0, 3
c.8, -2, 1, 3, 5, 4, 4, 1, 3, 3
d.0, 2, 0, 0, -1, 1, -2, 1, 0, -1, 1, -1, 0, -3,-2, -1, 0, 1
Question: Corporate sustainability of CPA firms.Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 1.28 (p. 51). Corporate sustainability, recall, refers to business practices designed around social and environmental considerations. Data on the level of support for corporate sustainability were obtained for 992 senior managers. The level of support was measured quantitatively. The simulation was used to convert the data from the study to a scale ranging from 0 to 160 points, where higher point values indicate a higher level of support for sustainability.
a.A histogram for level of support for sustainability is shown next. What type of histogram is produced, frequency or relative frequency?
b.Use the graph to estimate the percentage of the 992 senior managers who reported a high (100 points or greater) level of support for corporate sustainability.
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