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Chapter 3: Q9 (page 127)
Estimating s A large sample of sleep times includes values ranging from a low of 4 hours to a high of 10 hours. Use the range rule of thumb to estimate the standard deviation.
The estimated standard deviation obtained by using the range rule of thumb is 1.5 hours.
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:In Exercises 5鈥�20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as 鈥渕inutes鈥�) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.
Most Expensive Colleges Listed below in dollars are the annual costs of tuition and fees at the 10 most expensive colleges in the United States for a recent year (based on data from U.S. News & World Report). The colleges listed in order are Columbia, Vassar, Trinity, George Washington, Carnegie Mellon, Wesleyan, Tulane, Bucknell, Oberlin, and Union. What does this 鈥渢op 10鈥� list tell us about the variation among costs for the population of all U.S. college tuitions?
49,138 47,890 47,510 47,343 46,962 46,944 46,930 46,902 46,870 46,785
In Exercises 21鈥�24, find the mean and median for each of the two samples, then compare the two sets of results.
Parking Meter Theft Listed below are amounts (in millions of dollars) collected from parking meters by Brinks and others in New York City during similar time periods. A larger data set was used to convict five Brinks employees of grand larceny. The data were provided by the attorney for New York City, and they are listed on the Data and Story Library (DASL) website. Do the limited data listed here show evidence of stealing by Brinks employees?
Collection Contractor Was Brinks 1.3 1.5 1.3 1.5 1.4 1.7 1.8 1.7 1.7 1.6
Collection Contractor Was Not Brinks 2.2 1.9 1.5 1.6 1.5 1.7 1.9 1.6 1.6 1.8
In Exercises 21鈥�28, use the same list of Sprint airport data speeds (Mbps) given for Exercises 17鈥�20. Find the indicated percentile or quartile.
P40
In Exercises 5鈥�20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as 鈥渕inutes鈥�) in your results. (The same data were used in Section 3-1, where we found measures of center. Herewe find measures of variation.) Then answer the given questions.
Caffeine in Soft Drinks Listed below are measured amounts of caffeine (mg per 12oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, . . ., Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans?
0 0 34 34 34 45 41 51 55 36 47 41 0 0 53 54 38 0 41 47
Trimmed Mean Because the mean is very sensitive to extreme values, we say that it is not a resistant measure of center. By deleting some low values and high values, the trimmed mean is more resistant. To find the 10% trimmed mean for a data set, first arrange the data in order, then delete the bottom 10% of the values and delete the top 10% of the values, then calculate the mean of the remaining values. Use the axial loads (pounds) of aluminum cans listed below (from Data Set 30 鈥淎luminum Cans鈥� in Appendix B) for cans that are 0.0111 in. thick. An axial load is the force at which the top of a can collapses. Identify any outliers, then compare the median, mean, 10% trimmed mean, and 20% trimmed mean.
247 260 268 273 276 279 281 283 284 285 286 288
289 291 293 295 296 299 310 504
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