Chapter 4, Problem 4.5P

$\boxed{SOC}$ In problem 3.6, you computed mean and median income for the 13 Canadian provinces and territories and for 13 U.S. states in two separate years. Now compute the standard deviation and range for each year, and, taking account of the two measures of central tendency and the two measures of dispersion, write a paragraph summarizing the distributions. What do the measures of dispersion add to what you already knew about central tendency? Did the median income of the provinces and states become more or less variable over the period? The scores are reproduced here.

Median Income for Canadian Provinces and Territories, 2000 and 2011 (Canadian dollars)

Province or Territory	2000	2011
Newfoundland and Labrador	38,800	67,200
Prince Edward Island	44,200	66,500
Nova Scotia	44,500	66,300
New Brunswick	43,200	63,930
Quebec	47,700	68,170
Ontario	55,700	73,290
Manitoba	47,300	68,710
Saskatchewan	45,800	77,300
Alberta	55,200	89,930
British Columbia	49,100	69,150
Yukon Columbia	56,000	90,090
Northwest Territories	61,000	105,560
Nunavut	37,600	65,280
$\text{Mean}=$
$\text{Median}=$
$\text{Range}=$
$\text{Standard Deviation}=$

Median Income for Thirteen States, 1999 and 2012 (U.S dollars)

State	1999	2012
Alabama	36,213	43,464
Alaska	51,509	63,348
Arkansas	29,762	39,018
California	43,744	57,020
Connecticut	50,798	64,247
Illinois	46,392	51,738
Kansas	37,476	50,003
Maryland	52,310	71,836
Michigan	46,238	50,015
New York	40,058	47,680
Ohio	39,617	44,375
South Dakota	35,962	49,415
Texas	38,978	51,926
$\text{Mean}=$
$\text{Median}=$
$\text{Range}=$
$\text{Standard Deviation}=$

3.6 $\boxed{SOC}$ The following tables list the median family incomes for the 13 Canadian provinces and territories in 2000 and 2011 and for 13 states of the United States in 1999 and 2012. For the provinces and the states, compute the mean and median family income for each year and compare the two measures of central tendency. Which measure of central tendency is greater for each year? Are the distributions skewed? In which direction?

Median Income for Canadian Provinces and Territories, 2000 and 2011 (Canadian dollars)

Province or Territory	2000	2011
Newfoundland and Labrador	38,800	67,200
Prince Edward Island	44,200	66,500
Nova Scotia	44,500	66,300
New Brunswick	43,200	63,930
Quebec	47,700	68,170
Ontario	55,700	73,290
Manitoba	47,300	68,710
Saskatchewan	45,800	77,300
Alberta	55,200	89,930
British Columbia	49,100	69,150
Yukon Columbia	56,000	90,090
Northwest Territories	61,000	105,560
Nunavut	37,600	65,280
$\text{Mean}=$
$\text{Median}=$

Median Income for Thirteen States, 1999 and 2012 (U.S dollars)

State	1999	2012
Alabama	36,213	43,464
Alaska	51,509	63,348
Arkansas	29,762	39,018
California	43,744	57,020
Connecticut	50,798	64,247
Illinois	46,392	51,738
Kansas	37,476	50,003
Maryland	52,310	71,836
Michigan	46,238	50,015
New York	40,058	47,680
Ohio	39,617	44,375
South Dakota	35,962	49,415
Texas	38,978	51,926
$\text{Mean}=$
$\text{Median}=$