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.)