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Find the appropriate measure of central tendency for each variable displayed in problem 2.5. Report each statistic as you would in a formal research report. 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 = Problem 2.5: The scores of 15 respondents on four variables are as reported here. These scores were taken from a public-opinion survey called the General Social Survey (GSS), the data set used for the computer exercises in this text. For the actual questions, see Appendix G. The numerical codes for the variables are as follows: Sex Support for Gun Control Level of Education Age 1 = Male 2 = Female 1 = in favor 2 = Opposed 0 = Less than HS 1 = HS 2 = Jr. college 3 = Bachelor’s 4 = Graduate Actual years Case Number Gender Support for Gun Level of Education Age 1 2 1 1 45 2 1 2 1 48 3 2 1 3 55 4 1 1 2 32 5 2 1 3 33 6 1 1 1 28 7 2 2 0 77 8 1 1 1 50 9 1 2 0 43 10 2 1 1 48 11 1 1 4 33 12 1 1 4 35 13 1 1 0 39 14 2 1 1 25 15 1 1 1 23

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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 3.7P
Textbook Problem
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Find the appropriate measure of central tendency for each variable displayed in problem 2.5. Report each statistic as you would in a formal research report.

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 =

Problem 2.5: The scores of 15 respondents on four variables are as reported here. These scores were taken from a public-opinion survey called the General Social Survey (GSS), the data set used for the computer exercises in this text. For the actual questions, see Appendix G. The numerical codes for the variables are as follows:

Sex Support for Gun Control Level of Education Age
1 = Male
2 = Female
1 = in favor
2 = Opposed
0 = Less than HS
1 = HS
2 = Jr. college
3 = Bachelor’s
4 = Graduate
Actual years
Case Number Gender Support for Gun Level of Education Age
1 2 1 1 45
2 1 2 1 48
3 2 1 3 55
4 1 1 2 32
5 2 1 3 33
6 1 1 1 28
7 2 2 0 77
8 1 1 1 50
9 1 2 0 43
10 2 1 1 48
11 1 1 4 33
12 1 1 4 35
13 1 1 0 39
14 2 1 1 25
15 1 1 1 23

Expert Solution
To determine

To find:

The most appropriate measures of central tendency for each variable.

Explanation of Solution

Description:

When the variables measured have non-numerical scores or categories, they are said to have a nominal level of measurement.

When the variables measured have non-numerical scores or categories that could be ranked from high to low, they are said to have an ordinal level of measurement.

When the variables measured have numerical scores and can be used for further statistical analysis, they are said to have an interval ratio level of measurement.

From the given information, there are four variables Gender, Support for Gun Control, Level of Education, and Age. Here, the variable Age has a numeric value; therefore, the level of measurement of this variable is interval-ratio. The variables Gender and Support for Gun Control can be classified into categories; therefore, the level of measurement of these variables is Nominal. Further, the variable Level of Education can be classified into categories and can be ranked; therefore, the level of measurement is Ordinal.

Choosing a Measures of Central Tendency:

When the data is Nominal type — Mode

When the data is Ordinal type — Median

When the data is Interval ratio type — Mean

For the variable Age, the measure of central tendency is: Mean

Formula Used:

The formula to calculate mean is given by,

X¯=i=1NXiN

Substitute 15 for N, 45 for X1, 48 for X2 and so on in the above mentioned formula,

X¯=45+48+...+25+2315=61415=40.93

For the variable Gender, the measure of central tendency is: Mode.

Formula used:

The Mode:

The mode of any distribution of scores is the value that occurs most frequently

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