(For Questions 1, 2, & 3) When I was a graduate student in Arizona State University, I postulated the existence of a new elementary particle, which I named crazion, for convenience, that could explain the elusive dark matter in the interstellar space. I took a look at 29 interstellar regions, and found that the necessary mass of this crazion in each of the studied interstellar region (in unit of, Au, short for Aurum, for the sake of simplicity) as follow:

1.6, 1.8, 1.3, 2.4, 1.7, 1.7, 1.8, 1.4, 1.4, 1.6, 1.4, 2.0, 2.2, 2.1,

1.1, 1.3, 2.6, 2.7, 1.3, 1.6, 1.7, 1.7, 1.4, 1.9, 1.5, 1.7, 1.6, 1.9, 1.9

1. (5 points) Prepare a frequency distribution with a class width of 0.2 Au, and another with class width of 0.5 Au.
2. (5 points) Construct a histogram with a class width of 0.2 Au and another with a class width of 0.5 Au.
3. (5 points) Give a 5-number summary of the masses of the postulated crazions, and construct the corresponding boxplot.
4. (10 points) Of course, it is always nice to have the benefit of the raw data. With the given list of 29 crazion masses, you can easily determined the mean mass of the sample. But what if you do not have the benefit of the raw data set?
   Now pretend that you are only given a frequency distribution or just a histogram, and you are asked to find out the mean mass of the postulated crazions. Use what you have gotten in Question 1 and/or Question 2 to determine the mean mass of the postulated crazions. Do it with frequency table/histogram with class width of 0.2 Au, and again with 0.5 Au. Compare your results with the "actual" mean mass.
   (For Questions 5, 6 & 7) I have 5 gem-quality stishovite crystals in my home collection. Their weights, in carat, are 23.5, 14.6, 30.6, 10.8, 28.3.
5. (10 points) What is the variance in weight of my gem collection?
6. (10 points) What is the standard deviation in weight of my gem collection?
7. (10 points) What are the coefficients of variation in weight of my gem collection?
8. (10 points) If an agency conducts a survey on the choice of vegetable by Americans. It is reported by the agency that 57% of Americans prefer broccoli. Is this report descriptive or inferential? Please explain your answer.
9. (10 points) A supermarket is considering expanding its services by adding a pharmacy, but prior to doing so it will use a survey to determine the extent to which its customers are interested in such a service. The employees have provided four different suggested survey procedures:

1. Ask customers to voluntarily phone in their preferences.
2. Ask customers to voluntarily mail in their preferences.
3. Survey a selection of people whose names are randomly chosen from a list of all customers.
4. Survey a selection of people whose names are randomly chosen from the telephone directory.

Which survey procedure do you think would be the most appropriate for obtaining a statistically unbiased sample? Please explain your answer.

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