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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: Hotels’ use of ecolabels.Refer to the Journal of Vacation Marketing(January 2016) study of travelers’ familiaritywith ecolabels used by hotels, Exercise 2.42 (p. 94). Recallthat a sample of 392 adult travelers were shown a list of6 different ecolabels, and asked, “How familiar are youwith this ecolabel, on a scale of 1 (not familiar at all) to5 (very familiar).” The mean and standard deviation ofthe responses for each ecolabel are provided in the table.Which of the ecolabels had the most variation in numericalresponses? Explain.
Ecolabel | Mean | Std. Dev. |
Energy Star | 4.44 | 0.82 |
TripAdvisor | 3.57 | 1.38 |
Green Leaders Audubon | 2.41 | 1.44 |
International U.S Green | 2.28 | 1.39 |
Building Council Green Business | 2.25 | 1.39 |
Green Key | 2.01 | 1.30 |
Budget lapsing at army hospitals.Accountants use the term budget lapsingto describe the situation that occurs when unspent funds do not carry over from one budgeting period to the next. Due to budget lapsing, U.S. army hospitals tend to stockpile pharmaceuticals and other supplies toward the end of the fiscal year, leading to a spike in expenditures. This phenomenon was investigated in the Journal of Management Accounting Research(Vol. 19, 2007). Data on expenses per full-timeequivalent employees for a sample of 1,751 army hospitalsyielded the following summary statistics: xbar= \(6,563,m= \)6,232, s= \(2,484, QL = \)5,309 and QU = \(7,216.
a.Interpret, practically, the measures of relative standing.
b.Compute the interquartile range, IQR, for the data.
c.What proportion of the 1,751 army hospitals have expenses between \)5,309 and $7,216?
Salaries of bachelor’s degree graduates. PayScale, Inc., an online provider of global compensation data, conducts an annual salary survey of bachelor’s degree graduates. Three of the many variables measured by PayScale are the graduate’s current salary, mid-career salary, and the college or university where they obtained their degree. Descriptive statistics are provided for each of the over 400 colleges and universities that graduates attended. For example, graduates of the University of South Florida (USF) had a mean current salary of \(57,000, a median mid-career salary of \)48,000, and a mid-career 90th percentile salary of $131,000. Describe the salary distribution of USF bachelor’s degree graduates by interpreting each of these summary statistics.
Corporate sustainability of CPA firms.Refer to the Business and Society(March 2011) study on the sustainability behaviors of CPA corporations, Exercise 2.23 ( p. 83). Recall that level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each of 992 senior managers at CPA firms. Numerical measures of central tendency for level of support are shown in the accompanying Minitab printout.
Descriptive Statistics: Support | |||||||
Variable Support | N | Mean | Minimum | Median | Maximum | Mode | N for mode |
992 | 67.755 | 0.000 | 68.000 | 155.000 | 64 | 20 |
a.Locate the mean on the printout. Comment on the accuracy of the statement: “On average, the level of support for corporate sustainability for the 992 senior managers was 67.76 points.”
b.Locate the median on the printout. Comment on the accuracy of the statement: “Half of the 992 senior managers reported a level of support for corporate sustainability below 68 points.”
c.Locate the mode on the printout. Comment on the accuracy of the statement: “Most of the 992 senior managers reported a level of support for corporate sustainability below 64 points.”
d.Based on the values of the measures of central tendency, make a statement about the type of skewness (if any) that exists in the distribution of 992 support levels. Check your answer by examining the histogram shown in Exercise 2.23.
Calculate the variance and standard deviation for samples where
a.n= 10, ∑x2 = 84, ∑x= 20
b.n= 40, ∑x2 = 380, ∑x= 100
c.n= 20, ∑x2 = 18, ∑x= 17.
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