For problems 1 - 2 determine whether the given values are from discrete or continuous data set.
1. A statistics professor counts 3 absent students. Discrete Continuous
2. A statistics professor finds that on the first test, the first paper is turned in 39.6 minutes after the test began. Discrete Continuous
For problems 3 - 6 determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
3. The number of errors made when a Best Buy store scans 8000 different purchases Nominal Ordinal Interval Ratio
4. The years in which new editions of the book were published Nominal Ordinal Interval Ratio
5. Consumer Reports magazine ratings of "best buy, recommended, not recommended" Nominal Ordinal Interval Ratio
6. Distances traveled by students who commute to college Nominal Ordinal Interval Ratio
For problems 7 - 11 determine whether the given data are qualitative or quantitative.
7. Zip codes Qualitative Quantitative
8. The alphabetic list of students in a group Qualitative Quantitative
9. Social security numbers Qualitative Quantitative
10. Distances traveled by students who commute to college Qualitative Quantitative
11. Noon temperatures in Death Valley this week Qualitative Quantitative
For problems 12 - 14 determine whether the group is a sample or a population.
12. A small group of students from the class is selected, and the average (mean) age is 20.7 years.
13. All the state governors are surveyed, and 30 of them are found to be Democrats.
14. Several Domino sugar packs are randomly selected, and the average (mean) weight of the contents is 3,647 g.
Find the (a) mean, (b) median, (c) mode for the given data
15. 67 66 59 62 63 66 66 55
16. 16 14 14 14 13 19
17. Find the correspondence between three characteristics of the center (mean, median, mode) and their advantages/disadvantages.
a) Mean b) Median c) Mode A B C
Often a good choice if there are some extreme values and outliers.
Appropriate for some categorical data. For some sets of data it could be absent.
Works well with many statistical methods, especially for data without outliers.
18. Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee, but many people cheat. Researchers at Newcastle University replaced the picture of flowers on the wall behind the coffee station with a picture of staring eyes. They found that the average contribution increased significantly above the well-established standard when the people felt they were behind watched, even though the eyes were patently not real. Was this a sampling or an experiment? How can we tell?
Questions 19 - 21 are based on the sample of annual numbers of deaths from tornados in the United States from 1990 through 2000 : 53 39 39 33 69 30 25 67 130 94 40
19. Find mean and standard deviation.
20. Sketch a histogram.
21. Sketch a boxplot. Show the scale.
22. Identify the type of sampling (simple random sample, systematic, convenience, stratified, cluster) used when a sample of the 366,000 Coca Cola shareholders is obtained as described.
A. A complete list of all stockholders is compiled, and every 500th name is selected.
B. At the annual stockholders' meeting, a survey is conducted of all who attend.
C. Fifty different stockholders are randomly selected, and a survey is made of all their clients who own shares of Coca Cola.
D. A computer file of all stockholders is compiled so that they are all numbered consecutively, then random numbers generated by computer are used to select the sample of stockholders.
E. All of the stockholders' zip codes are collected, and five stockholders are randomly selected from each zip code.
Find the 5-number summary (Min, Q1, Median, Q3, Max).
23. 4 9 9 9 8 7 1 5 4 4 4 7 6 7 7 23
24. Bar charts and histograms look similar. Will you use both of them for qualitative and quantitative variables or not? For what types of data will you use bar charts, and for what types of data will you use histograms? Write your explanation.
25. Question #25 is based on the following: One measure of the size of an automobile engine is its "displacement", the total volume of its cylinders. Summary statistics for several models of new cars are shown. These displacements were measures in cubic inches. Summary of Displacement Count 38 Mean 177.29 Median 148.5 StdDev 88.88 Q1 105 Q3 231 a. How many cars were measured? b. What is the interquartile range (IQR)? c. Why might the mean be so much larger than the median? Explain.