Problem Set 2

Due Monday, February 2, 2004

Note: If you hand this problem set in on Friday, January 30, Mark Nelson, the student assistant for the class, will attempt to mark the problem set by Tuesday morning, February 3. If handed in on Monday, February 2, it may not be marked prior to the midterm examination. Model answers will be available on the web site on February 3 so all problem sets are to be handed in by then.

1. Distribution of age last worked. Table 1 contains information about the age at which survey respondents last did paid work. These data come from 4,297 respondents in Statistics Canada, General Social Survey, 2001: Family History, a cross-Canada survey of adults. Table 1 gives the frequency distribution for the number of respondents who reported each age at which they last did paid work, for each of male respondents and females respondents. Using these data

Construct histograms for the distribution of age last did paid work for each of males and females.
What is the mean and median age for (i) males and (ii) females? (For the open-ended interval, assume that all quit paid work at age 65).
In words, briefly describe similarities and differences between the two distributions.

Table 1. Frequency distributions of age when respondent last did paid work

Age in years	Number of respondents by sex
Age in years	Male	Female
15-24	40	521
25-34	103	687
35-44	168	435
45-54	266	509
55-59	253	319
60-64	317	259
65 plus	238	182
Total	1,385	2,912

Source: Statistics Canada, General Social Survey, Cycle 15

2. Length of time using internet. The bar charts of Figures 1 and 2 come from “Better things to do or dealt out of the game? Internet dropouts and infrequent users,” by Susan Crompton, Jonathan Ellison, and Kathryn Stevenson, in Statistics Canada, Canadian Social Trends, Summer 2002, p. 5. For each group of users, what is the (a) mode and (b) interquartile range of length of time using internet? Explain or show your calculations.

3. Extent of use of internet. Using the data in Table 2, obtain the mean, median, range, variance, and standard deviation for each of the variables (a) number of times used internet in last month, and (b) number of hours used internet in past week.

Table 2. Use of internet in last month and past week, ten respondents

Identification number	Number of times used internet in last month	Number of hours used internet in past week
1	30	3
2	12	4
3	28	10
4	30	22
5	27	7
6	3	1
7	6	1
8	15	2
9	10	2
10	27	10

Source: Random sample from Saskatchewan respondents surveyed in Statistics Canada, 2000 General Social Survey, Cycle 14: Access to and Use of Information Communication Technology

4. Averages and percentiles

a. While the word average is not contained in the following newspaper headlines, each could be taken to imply one of the mode, median, or mean. For each headline, state which of the three concepts of average is relevant and explain why.

We’re worth $3.9 trillion: $121,900 for each Canadian. Leader-Post, September 27, 2003, p. B4.

Witness says Thatcher no risk to most people. Moose Jaw Times-Herald, September 26, 2003, p. 1.

b. The Leader-Post of January 20, 2004 had an article with headlines “Property-Tax Survey,” and “Regina ranks near middle.” The article stated

The survey suggests that total property taxes in Regina for a sample home were $2,265 in 2003, putting the capital 16^th of the 25 cities reviewed (with first place being cheapest).

In a sentence or two, explain how this relates to measures of central tendency and percentiles?

c. The Leader-Post of September 30, 2003, on p. A1, reports on the coldest, warmest, windiest and wettest cities of Canada. Explain what percentile of dryness is implied for (i) Saskatoon and (ii) Regina in the following:

… the report says only six cities out of the 100 studied are drier and Saskatoon and only 11 are drier than Regina.