Question

Problem # 9: Family income 2011 According to Statistics Canada, Income Statistics Division, the mean after-tax family income in 2011 was $63000, while the median was $50700. In contrast to 2011 dollars, the mean and median in 1980 were $50000 and $49500 respectively. 1. Why did you expect to find a higher mean than median in both years? Draw a very rough plot of what the histogram for 2011 incomes might look like. 2. How much higher was the mean compared with the median in 2011, in percentage terms? How much higher in 1980? What does this suggest about how the income distribution has changed in Canada? Draw two very rough histograms to represent what the two distributions might look like in comparison to each other. Are the rich getting richer, and the poor poorer? Explain your answer. 3. Suppose that in 2030, the mean and median in actual 2030 dollars are $80000 and $60000 respectively. Have the rich gotten richer, and the poor poorer? Say what you can about what appears to be going on with incomes, based on this limited information.

Answer 1

1)

The Salary histogram is expected to have a longer tail on the right side which will pull the mean salary higher than Median value. We expect the histogram to look like:

2)

Year	Mean	Median	% Higher
2011	63,000	50,700	24.3%
1980	50,000	49,500	1.0%

From the above data, yes we can conclude that rich are getting richer, and the poor poorer. This is evident from the relative increase in Mean Salary in 2011 as compared to 1980

3)

Year	Mean	% Inc in Mean	Median	% Inc in Median
2030	80,000	27%	60,000	18%
2011	63,000	26%	50,700	2%
1980	50,000		49,500

After considering the 2030 data, we cannot conclude that rich are getting richer, and the poor poorer as from the above table it is clear that median value has increased significantly from 2011 while Mean has increased at the same rate.