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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Best-paid CEOs.Refer to Glassdoor Economic Research firm’s 2015 ranking of the 40 best-paid CEOs in Table 2.1 (p. 65). Recall that data were collected on a CEO’s current salary, age, and the ratio of salary to a typical worker’s pay at the firm.
a.Create a scatterplot to relate a CEO’s ratio of salary to worker pay to the CEO’s age. Comment on the strength of the association between these two variables.
b.Conduct an outlier analysis of the ratio variable. Identify the highly suspect outlier in the data.
c.Remove the highly suspect outlier from the data and recreate the scatterplot of part a. What do you observe?
Question: The output from a statistical software package indicates that the mean and standard deviation of a data set consisting of 200 measurements are \(1,500 and \)300, respectively.
a.What are the units of measurement of the variable of interest? Based on the units, what type of data is this: quantitative or qualitative?
b.What can be said about the number of measurements between \(900 and \)2,100? Between \(600 and \)2,400? Between \(1,200 and \)1,800? Between \(1,500 and \)2,100?
For each of the following data sets, compute xbar, s2, and s. If appropriate, specify the units in which your answers are expressed.
a.4, 6, 6, 5, 6, 7
b.- \(1, \)4, - \(3, \)0, - \(3, - \)6
c.3/5 %, 4/5 %, 2/5 %, 1/5 %, 1/16 %
d.Calculate the range of each data set in parts a–c.
Voltage sags and swells.Refer to the Electrical Engineering(Vol. 95, 2013) study of power quality (measured by“sags” and “swells”) in Turkish transformers, Exercise 2.96(p. 116). For a sample of 103 transformers built for heavyindustry, the mean and standard deviation of the numberof sags per week were 353 and 30, respectively; also, themean and standard deviation of the number of swells perweek were 184 and 25, respectively. Consider a transformerthat has 400 sags and 100 swells in a week.
a.Would you consider 400 sags per week unusual, statistically? Explain.
b.Would you consider 100 swells per week unusual, statistically? Explain.
Question: State SAT scores.Refer to Exercise 2.27 (p. 84) and the data on state SAT scores. Construct a scatterplot for the data, with the 2010 Math SAT score on the horizontal axis and the 2014 Math SAT score on the vertical axis. What type of trend do you detect?
State | 2010 Math SAT | 2014 Math SAT |
Alabama | 538 | 550 |
Alaska | 503 | 513 |
Arizona | 527 | 524 |
Arkansa | 571 | 564 |
California | 510 | 516 |
Wisconsin | 608 | 603 |
Wyoming | 599 | 565 |
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