ECON 1203 Tutorial Workshop
1. (a) What is meant by a variable in a statistical sense? Distinguish between qualitative and quantitative statistical variables, and between continuous and discrete variables. Give examples.
(b) Distinguish between (i) a statistical population and a sample; (ii) a parameter and a statistic. Give examples.
2. In order to know the market better, the second-hand car dealership, Anzac Garage, wants to analyze the age of second-hand cars being sold. A sample of 20 advertisements for passenger cars is selected from the second-hand car advertising/listing website www.drive.com.au The ages in years of the vehicles at time of advertisement are listed below:
5, 5, 6, 14, 6, 2, 6, 4, 5, 9, 4, 10, 11, 2, 3, 7, 6, 6, 24, 11
(a) Calculate the frequency, cumulative frequency and relative frequency distributions for the age data using the following bin classes: More than 0 to less than or equal to 8 years More than 8 to less than or equal to 16 years More than 16 to less than or equal to 24 years.
(b) Sketch a frequency histogram using the calculations in part (a). What can you say about the distribution of the age of these second-hand cars? Is there anything that concerns you about the frequency table and histogram? Specifically, is the choice of bin classes appropriate? What needs to be done differently?
(c) Halve the width of the bins (0 to 4, 4 to 8, etc) and recalculate the frequency, cumulative frequency and relative frequency distributions. Using the new distributions and histogram, what can you now say about the distribution of the age of second-hand cars?
3. Health expenditure A recent report by Access Economics provides a comparison of Australian expenditures on health with that of comparable OECD countries. Data from that report relating to the year 2005 have been used to reproduce their Figure 2.2 (below denoted as Figure 2.1).
(a) What are the key features of these data?
(b) While this is a bivariate scatter plot, there are three variables involved: health expenditure, GDP and population. Why account for population by expressing health expenditure and GDP in per capita terms?