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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 distribution skewed? In which direction? Median Income for Canadian Provinces and Territories, 2000 and 2011 (Canadians 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 56,000 90,090 Northwest Territories 61,000 105,560 Nunavut 37,600 65,280 Mean = Median = Source: Statistics Canada. Retrieved from http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/famil108-eng-htm 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 Mean = Median = Sources: 1999: U.S. Bureau of the Census. Statistical Abstract of the United States:2001 .p. 436. Retrieved from http://www.census.gov/prod/2002pubs/01statab/income.pdf.2012:U.S. Bureauof the Census. American Community Survey.2012 . Retrieved form http://www.census.gov/hhes/www/income/data/statemedian/

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Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
BuyFind

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

Solutions

Chapter
Section
Chapter 3, Problem 3.6P
Textbook Problem
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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 distribution skewed? In which direction?

Median Income for Canadian Provinces and Territories, 2000 and 2011 (Canadians 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 56,000 90,090
Northwest Territories 61,000 105,560
Nunavut 37,600 65,280
Mean =
Median =

Source: Statistics Canada. Retrieved from http://www.statcan.gc.ca/tables-tableaux/sum-som/l01/cst01/famil108-eng-htm

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
Mean =
Median =

Sources: 1999: U.S. Bureau of the Census. Statistical Abstract of the United States:2001.p. 436. Retrieved from http://www.census.gov/prod/2002pubs/01statab/income.pdf.2012:U.S. Bureauof the Census. American Community Survey.2012. Retrieved form http://www.census.gov/hhes/www/income/data/statemedian/

Expert Solution
To determine

To find:

The most appropriate measures of central tendency for each variable.

Explanation of Solution

Provinces and Territories:

For year 2000:

Mean:

The formula to calculate mean is given by,

X¯=i=1NXiN

Substitute 13 for N, 38, 800 for X1, 44, 200 for X2 and so on in the above mentioned formula,

X¯=38,800+44,200+...+61,000+37,60013=62610013=48161.54

Median:

Arrange the data in ascending order.

The number of terms is 13, which is odd.

The median for the odd number of terms is given by,

Median=(Number of terms+1)2

Substitute 13 for number of terms in the above mentioned formula,

Median=(13+1)2=142=7

The median corresponding to 7th number from the ordered data is 47, 300.

Therefore, the median is 47, 300.

For year 2011,

Mean:

The formula to calculate mean is given by,

X¯=i=1NXiN

Substitute 13 for N, 37, 200 for X1, 66, 500 for X2 and so on in the above mentioned formula,

X¯=67,200+66,500+...+105,560+65,28013=97141013=74723.85

Median:

Arrange the data in ascending order.

The number of terms is 13, which is odd.

The median for the odd number of terms is given by,

Median=(Number of terms+1)2

Substitute 13 for number of terms in the above mentioned formula,

Median=(13+1)2=142=7

The median corresponding to 7th number from the ordered data is 68, 710.

Therefore, the median is 68, 710.

State:

For year 1999,

Mean:

The formula to calculate mean is given by,

X¯=i=1NXiN

Substitute 13 for N, 36, 213 for X1, 51, 509 for X2 and so on in the above mentioned formula,

X¯=36,213+51,509+...+35,962+38,97813=54905713=42235

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