Reference no: EM131017395

A. (For Questions 1, 2, & 3) There are 31 participants in a special high-adventure camp at Goshen Scout Camp last September. Following is a list of the age of the participants.

16, 18, 13, 24, 17, 17, 18, 14, 14, 16, 14, 20, 22, 21, 15
11, 13, 26, 27, 13, 16, 17, 17, 14, 19, 15, 17, 16, 19, 19, 28

1. Prepare a frequency distribution table of the participants' ages with a class width of 2 years, and another with class width of 5 years. Make a table with column #1 with an age range and column #2 with the frequency of that age range, and column #3 with the cumulative frequency. Be sure that the sum of the frequencies add up to 31 and the sum of the relative frequencies add up to 1. Use at least 4 decimal places in your computations.

Range of Age in Years	Frequency	Relative Frequency	Cumulative Frequency
10.0 to 11.9
12.0 to 13.9
14.0 to 15.9
16.0 to 17.9
18.0 to 19.9
20.0 to 21.9
22.0 to 23.9
24.0 to 25.9
26.0 to 27.9
28.0 to 29.9
Total

Range of Age in Years	Frequency	Relative Frequency	Cumulative Frequency
10.0 to 14.9
15.0 to 19.9
20.0 to 24.9
25.0 to 29.9
Total

2. Construct a histogram of the participants' age with a class width of 2 years and another with a class width of 5 years. Let the horizontal axis be "age" and the vertical axis be "number of participants". Use a graphing utility to draw the two histograms! What can we say about the choice of class width?

3. Give a 5-number summary (min, Q1, median, Q3, max) of the ages of the participants (i.e. the raw data), and construct the corresponding boxplot with the Boxplot 1 graphing utility in "Statistics and Probability Applets".

B. (For Questions 4 & 5) Below please find a hypothetical (imaginary) data set for the enrollment number in our three statistics classes over the past few years. Please note that STAT 225 was not in existence until the fall of 2006.

	STAT 200	STAT 225	STAT 230
Spring 2006	335	-----	388
Summer 2006	191	-----	178
Fall 2006	404	141	445
Spring 2007	406	154	463
Summer 2007	225	43	218
Fall 2007	308	129	352
Spring 2008	320	81	314
Summer 2008	196	42	156
Fall 2008	324	80	347
Spring 2009	375	92	332
Summer 2009	233	50	204
Fall 2009	406	112	334
Spring 2010	432	114	336
Summer 2010	230	49	203
Fall 2010	414	121	317
Spring 2011	498	119	318
Summer 2011	250	55	174
Fall 2011	544	140	196
Spring 2012	554	166	365
Summer 2012	317	82	185
Fall 2012	546	168	372
Spring 2013	643	134	312

I don't want you to waste your time punching in the numbers. So there is an attached Exel spreadsheet that you can use for this question. You can make the plot using Exel or transfer the data to another plotting program.

4. There are many graphical format to illustrate a given data set. However, some formats are better than others in the sense that they convey important and relevant information in the given data set. For the given data set, pick the most appropriate graphic format to present the above data set, and plot the given data. Feel free to include additional information you can deduce from the data set that you think can be useful make your point. Use the data in "sheet 1" of the Excel file.

5. At times, there may be unwarranted features in the plots you come up with, even though they are true representation of the given data. We may recall that data noise will distract us from conveying essential information in the data set. Do you encounter this situation in your plot? If so, what would you do to minimize distractions without misrepresenting the data? (For example, you could just plot the enrollment per academic year, or calendar year, by summing up the numbers for each "year", instead of plotting the enrollment for each session.) Use the data in "sheet 2" of the Excel file.

C. (For Questions 6, 7, & 8) I have a collection of 5 ancient gold coins. Their weights, in ounces, are 23.1, 18.6, 33.5, 12.4, and 27.1.

6. What is the mean weight of my ancient gold coins?

7. How do you consider this collection, a population or a sample? Why?

8. What is the variance (σ2) and standard deviation (σ) in weight of my coin collection? (Remember, depending on whether you consider this collection a population or a sample, you divide by N or (N-1) in the standard deviation calculation.)