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Chapter 3: Q7 (page 127)
Sleep Q3 For a sample of 80 sleep times, approximately how many of those times are less than Q3?
The observations of 60 sleep times in 80 would be less than the third quartile.
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Critical Thinking. For Exercises 5鈥�20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question.
California Smokers In the California Health Interview Survey, randomly selected adults are interviewed. One of the questions asks how many cigarettes are smoked per day, and results are listed below for 50 randomly selected respondents. How well do the results reflect the smoking behavior of California adults?
9 10 10 20 40 50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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
Heights The boxplot shown below results from the heights (cm) of males listed in Data Set 1 鈥淏ody Data鈥� in Appendix B. What do the numbers in that boxplot tell us?
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.
Fireighter Fatalities Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while fighting forest fires. The numbers are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of variation?
20 18 23 30 20 12 24 9 25 15 8 11 15 34
In Exercises 37鈥�40, refer to the frequency distribution in the given exercise and find the standard deviation by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviations to these standard deviations obtained by using Formula 3-4 with the original list of data values: (Exercise 37) 11.5 years; (Exercise 38) 8.9 years; (Exercise 39) 59.5; (Exercise 40) 65.4.
Standard deviation for frequency distribution
Blood Platelet Count of Males | Frequency |
0-99 | 1 |
100-199 | 51 |
200-299 | 90 |
300-399 | 10 |
400-499 | 0 |
500-599 | 0 |
600-699 | 1 |
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