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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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Consider the following three measurements: 0, 4, and 12. Find the z-score for each measurement if they are from a population with the following mean and standard deviation equal to
a.碌 = 2 and 蟽 = 1
b.碌 = 4 and 蟽 = 2
c.碌 = 8 and 蟽 = 2
d.碌 = 8 and 蟽 = 8
Products 鈥淢ade in the USA.鈥濃�淢ade in the USA鈥� is a claim stated in many product advertisements or on product labels. Advertisers want consumers to believe that the product is manufactured with 100% U.S. labor and materials鈥攚hich is often not the case. What does 鈥淢ade in the USA鈥� mean to the typical consumer? To answer this question, a group of marketing professors conducted an experiment at a shopping mall (Journal of Global Business, spring 2002). They asked every fourth adult entrant to the mall to participate in the study. A total of 106 shoppers agreed to answer the question, 鈥溾�楳ade in the USA鈥� means what percentage of U.S. labor and materials?鈥� The responses of the 106 shoppers are summarized as follows: 鈥�100%鈥� (64 shoppers), 鈥�75 to 99%鈥� (20 shoppers), 鈥�50 to 74%鈥� (18 shoppers), and 鈥渓ess than 50%鈥� (4 shoppers).
a.What type of data-collection method was used?
b.What type of variable, quantitative or qualitative, is measured?
c.Present the data in graphical form. Use the graph to make a statement about the percentage of consumers who believe 鈥淢ade in the USA鈥� means 100% U.S. labor and materials.
Question: Performance of stock screeners.Refer to the American Association of Individual Investors (AAII) statistics on stock screeners, Exercise 2.44 (p. 95). Annualized percentage return on investment (as compared to the Standard & Poor鈥檚 500 Index) for 13 randomly selected stock screeners are reproduced in the table.
(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.Find the range of the data for the 13 stock screeners. Give the units of measurement for the range.
b.Find the variance of the data for the 13 stock screeners. If possible, give the units of measurement for the variance.
c.Find the standard deviation of the data for the 13 stock screeners. Give the units of measurement for the standard deviation
U.S. wine export markets.The Center for International Trade Development (CITD), provides a listing of the top 30 U.S. export markets for sparkling wines. Data on the amount exported (thousands of dollars) and 3-year percentage change for the 30 countries in a recent year are saved in the WINEXfile. (Data for 5 countries are listed in the table.) Descriptive statistics for these variables are shown in the Minitab printout (next column).
5 of the Top 30 U.S. Sparkling Wine Export Markets
Country | Export ($ Thousands) | 3-Year Change (%) |
Canada Japan Mexico Cayman Islands United Kingdom | 4952 3714 2104 1576 1041 | 71.9% -16.9 143.2 280.7 465.8 |
a.Locate the mean amount exported on the printout and practically interpret its value.
b.Locate the median amount exported on the printout and practically interpret its value.
c.Locate the mean 3-year percentage change on the printout and practically interpret its value.
d.Locate the median 3-year percentage change on the printout and practically interpret its value.
| Descriptive Statistics: Exports, Change | ||||||||||
Variable | N | N* | Mean | St Dev. | Min. | Q1 | Median | Q3 | Max. | IQR |
Export Change | 30 28 | 0 2 | 653 481 | 1113 1098 | 70 -49 | 105 21 | 231 156 | 523 499 | 4952 5750 | 418 478 |
e. Use the information on the printout to find the range of the amount exported.
f.Locate the standard deviation of the amount exported on the printout.
g.Use the result, part f, to find the variance of the amount exported.
h.If one of the top 30 countries is selected at random, give an interval that is likely to include the export amount for this country.
Give the percentage of measurements in a data set that are above and below each of the following percentiles:
a. 75th percentile
b. 50th percentile
c. 20th percentile
d. 84th percentile
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