Chapter 2: Q. 67 (page 137)
Of the three measures, which tends to reflect skewing the most, the mean, the mode, or the median? Why?
The outliers have the greatest impact on the mean, therefore mean tends to reflects skewing the most.
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a. For runners in a race, a low time means a faster run. The winners in a race have the shortest running times. Is it more desirable to have a finish time with a high or a low percentile when running a race?
b. The percentile of run times in a particular race is minutes. Write a sentence interpreting the percentile in the context of the situation.
c. A bicyclist in the percentile of a bicycle race completed the race in hour and minutes. Is he among the fastest or slowest cyclists in the race? Write a sentence interpreting the percentile in the context of the situation.
In a survey collecting data about the salaries earned by recent college graduates, Li found that her salary was in the percentile. Should Li be pleased or upset by this result? Explain
Use the following information to answer the next two exercises. Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.
Looking at your box plot, does it appear that the data are concentrated together, spread out evenly, or concentrated in some areas, but not in others? How can you tell?
Six hundred adult Americans were asked by telephone poll, "What do you think constitutes a middle-class income?" The results are in Table 2.69. Also, include left endpoint, but not the right endpoint.
a. What percentage of the survey answered "not sure"?
b. What percentage think that middle-class is from \(25,000 to \)50,000? c. Construct a histogram of the data.
i. Should all bars have the same width, based on the data? Why or why not?
ii. How should the <20,000 and the 100,000+ intervals be handled? Why? d. Find the 40th and 80th percentiles
e. Construct a bar graph of the data
The following data show the different types of pet food stores in the area carry. Calculate the sample mean and the sample standard deviation to one decimal place using a calculator.
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