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# Descriptive Statistics

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(For Questions 1, 2, 3, 4) We want to understand the weight distribution of lemons. You go to the supermarket and randomly select 29 lemons. Their weight, in ounces, is as follows:
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
1.1, 1.3, 1.3, 1.3, 1.4, 1.4, 1.4, 1.4, 1.5, 1.6, 1.6, 1.6, 1.6, 1.7, 1.7,
1.7, 1.7, 1.7, 1.8, 1.8, 1.9, 1.9, 1.9, 2.0, 2.1, 2.2, 2.4, 2.6, 2.7

1. Are the ounces from a discrete or continuous data set? Please provide an explanation for your answer.
2. What is the level of measurement (nominal, ordinal, interval, or ratio) of the data? Please provide an explanation for your answer.
3. Is it a sample or a population? If it is a sample, is it likely to be representative of the population?
4. Prepare a frequency distribution with a class width of 0.2 ounces, and another with class width of 0.5 ounces. Prepare a frequency distribution with a class width of 0.2 ounces
5. Construct a histogram with a class width of 0.2 ounces and another with a class width of 0.5 ounces.
6. Give a 5-number summary of the ounces of the lemons, and construct the corresponding boxplot.
7. Of course, it is always nice to have the benefit of the raw data. With the given list of weights of 29 lemons, you can easily determined the mean ounces 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 weight of the lemons. Use what you have gotten in Question 4 and/or Question 5 to determine the mean weight of the lemons. Do it with frequency table/histogram with class width of 0.2 ounces, and again with 0.5 ounces. Compare your results with the "actual" mean weight.

(For Questions 8, 9, and 10) I have 5 gem-quality crystals in my home collection. Their weights, in carats, are: 23.5, 14.6, 30.6, 10.8, and 28.3.

8. What is the variance in weight of my gem collection?
9. What is the standard deviation in weight of my gem collection?
10. What are the coefficients of variation in weight of my gem collection?