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Chapter 2: Q91. (page 116)
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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Business marketing publications.Business-to-business marketing describes the field of marketing between multiple business entities. The Journal of Business-to-Business Marketing (Vol. 15, 2008) produced a pie chart describing the number of business-to-business marketing articles published in all journals, by topical area, between 1971 and 2006. The data used to produce the pie chart are shown in the table.
Area | Number |
Global Marketing Sales Management Buyer Behavior Relationships Innovation Marketing Strategy Channels/Distribution Marketing Research Services | 235 494 478 498 398 280 213 131 136 |
Total | 2,863 |
a.Compute the relative frequencies for the nine topical areas shown in the table. Interpret the relative frequency for Buyer Behavior.
b.Use the relative frequencies, part a, to construct a pie chart for the data. Why is the slice for Marketing Research smaller than the slice for Sales Management?
Explain why we generally prefer the standard deviation to the range as a measure of variability for quantitative data.
Parents Against Watching Television.A society called Parents Against Watching Television (PAWT) is primarily concerned with the amount of television viewed by today’s youth. It asked 300 parents of elementary school aged children to estimate the number of hours their child spent watching television in any given week. The mean and the standard deviation for their responses were 17 and 3, respectively. PAWT then constructed a stem-and-leaf display for the data, which showed that the distribution of the number of hours was a symmetric, mound-shaped distribution. Identify the interval where you believe approximately 95% of the television viewing times fell in the distribution.
Question: For a set of data with a mound-shaped relative frequency distribution, what can be said about the percentage of the measurements contained in each of the intervals specified in Exercise 2.72?
Do social robots walk or roll?Refer to the International Conference on Social Robotics(Vol. 6414, 2010) study onthe current trend in the design of social robots, Exercise 2.5(p. 72). Recall that in a random sample of social robotsobtained through a Web search, 28 were built with wheels.The number of wheels on each of the 28 robots is listed inthe accompanying table.
(4 4 3 3 3 6 4 2 2 2 1 3 3 3 3 4 4 3 2 8 2 2 3 4 3 3 4 2)
Source:Based on S. Chew et al., “Do Social Robots Walk or Roll?” International Conference on Social Robotics, Vol. 6414, 2010 (adapted from Figure 2).
a.Generate a histogram for the sample data set. Is the distribution of number of wheels mound-shaped and symmetric?
b.Find the mean and standard deviation for the sample data set.
c.Form the interval, xbar ±2s.
d.According to Chebychev’s Rule, what proportion of sample observations will fall within the interval, part c?
e.According to the Empirical Rule, what proportion of sample observations will fall within the interval, part c?
f.Determine the actual proportion of sample observations that fall within the interval, part c. Even though the histogram, part a, is not perfectly symmetric, does the Empirical Rule provide a good estimate of the proportion?
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