Note: If you hand this problem set in on Friday, October 1, we will attempt to have it marked by October 5. If handed in on Monday, October 4, it will likely not be marked prior to the midterm examination. Model answers will be available on the web site and on reserve in the Library on the morning of October 5, so all problem sets are to be handed in by then.
1. Annual hours spent volunteering. Given the large range of values for the number of hours volunteered in the stem-and-leaf displays of Problem Set 1, I regrouped the frequency distributions into the format of Table 1 to reduce the size of the frequency distribution table. Using the frequency distributions of Table 1, construct the histogram of annual hours spent volunteering for each age group. Obtain the mode of number of hours spent volunteering for each age group.
2.
Record-setting cold. The Leader-Post of
January 29, 2004 (p. A1) reported record-setting cold for many parts of the
province. The temperatures reported for
seven locations are in Table 2 – in order to avoid dealing with negative
values, all temperatures are in degrees below zero Celsius. Use these data to compute the range, mean,
and standard deviation for the (a) new record temperature, and (b) old record
temperature. Also, for each of the new
and old record temperatures, explain which location has the median temperature.
3. Health status and income level. Table 3 provides percentage distributions of self-reported health status of Saskatchewan respondents, classified by household income. For respondents in the lowest income group (under $20,000), obtain the mode, median, mean, and interquartile range of health status. Obtain the same statistics for those in the highest income group ($60,000 plus). In words, briefly compare these two distributions.
4. Household incomes of volunteers and
non-volunteers. The frequency distributions
in Table 4 provide information concerning the household incomes of volunteers
and non-volunteers. The numbers in the
table are adapted from data about Saskatchewan respondents in the National Survey of Giving, Volunteering and
Participating, 1997, conducted by Statistics Canada. Compute the mean, median and seventy-fifth percentile
for each of volunteers and non-volunteers.
In a few sentences, compare the two distributions using these statistics
and the information in Table 4.
5. Averages. Below are four quotes that either contain the word “average” or imply some average. For each quote, write a short note explaining which average is likely being referred to or which average is implied.
a. “Unfortunately, the average student who is not athletically inclined wastes eight to 10 hours each week standing in the halls or socializing in the cafeteria.” Barrie Shelpley, “Tote that laundry, lift that bale: fitting in fitness,” The Globe and Mail, September 21, 2004, p. A17.
b. In an editorial in the September 21, 2004 issue of the Leader-Post, p. B7, Dave MacLean of the Canadian Taxpayer’s Federation is quoted as saying “when you have bureaucrats at all levels of government making more than the average Joe out there … there’s something not quite right on the cost side of government.” Later in the editorial the writer states “the utility Crowns employ thousands of people with high technical skills far beyond the level of the ‘average Joe’.”
c. “Traditionally, marriage was the only acceptable social institution for couples.”
d. “Individuals are postponing union formation until later than did earlier generations.”
Last two quotes from “Couples living apart” by Anne
Milan and Alice Peters, in the Statistics Canada publication, Canadian Social Trends, Summer 2003, pp.
2 and 3.
.Table 1.
Annual hours spent volunteering, 15-24 and 55-64 year olds,
Saskatchewan, 2000
|
Hours |
Frequency for age group: |
|
|
15-24 |
55-64 |
|
|
0-4 |
11 |
2 |
|
5-9 |
7 |
2 |
|
10-19 |
7 |
3 |
|
20-29 |
5 |
3 |
|
30-59 |
10 |
5 |
|
50-69 |
7 |
7 |
|
70-99 |
5 |
5 |
|
100-129 |
6 |
4 |
|
130-189 |
0 |
4 |
|
Total |
58 |
35 |
Table 2.
Temperatures in degrees below zero Celsius, selected Saskatchewan
locations
|
Location |
New record |
Old record |
|
Regina |
41.6 |
38.9 |
|
Saskatoon |
44.9 |
43.3 |
|
Estevan |
41.3 |
37.2 |
|
Weyburn |
40.9 |
37.8 |
|
Elbow |
38.6 |
37.8 |
|
Watrous |
43.3 |
42.2 |
|
Rosetown |
42.1 |
41.7 |
Source: Regina Leader-Post, January 29, 2004, p. A1
Table 3. Percentage of respondents with each level of
health status, classified by household income.
Saskatchewan respondents.
|
Health status |
Household income |
Total |
||
|
Under $20,000 |
$20,000 to $60,000 |
$60,000 plus |
||
|
Poor (1) |
6.1 |
1.2 |
0.4 |
2.0 |
|
Fair (2) |
9.4 |
8.9 |
1.6 |
6.9 |
|
Medium (3) |
41.2 |
29.1 |
20.6 |
29.2 |
|
Good (4) |
32.2 |
36.1 |
47.6 |
38.6 |
|
Excellent (5) |
11.1 |
24.7 |
29.8 |
23.3 |
|
Total |
100.0 |
100.0 |
100.0 |
100.0 |
|
Number of cases |
180 |
429 |
252 |
861 |
Source: Statistics Canada, General Social Survey, Cycle 14
Table 4. Frequency distributions
of volunteers and non-volunteers, classified by household income. Saskatchewan respondents, 1997
|
Income in thousands of dollars |
Number of respondents |
|
|
Volunteer |
Non-volunteer |
|
|
Under 20 |
230 |
132 |
|
20-40 |
278 |
119 |
|
40-60 |
247 |
61 |
|
60-80 |
185 |
51 |
|
80 plus |
56 |
8 |
|
Total |
996 |
371 |
Source: Adapted from Statistics Canada. National Survey of Giving, Volunteering and
Participating, 1997: Main file [machine readable data file]. Ottawa, Ontario, Statiswtics Canada. August 20, 1999.