central tendency measures

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sample problems and discussion of levels of measurement

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1 Variable = anything that can vary Attribute (or Value) = the ways it varies Working with a Single Variable Attributes vary in terms of their “level of measurement”

Levels of Measurement :

2 Levels of Measurement Nominal Ordinal Ratio Qualitative Quantitative more than / less than equidistant intervals “true 0” X X X X X Note: there is another called “interval” level of measurement. But I will not confuse you with that at the moment.

Levels of Measurement (definitions and examples):

3 Levels of Measurement (definitions and examples) Nominal Ordinal Ratio Qualitative differences: Attributes of variable differ only in KIND. Fruit: (apples, oranges, grapes) Sex: (male, female) Quantitative difference, but attributes can only be placed in ORDER (as in “more than” or “less than”) Course Grades: (As, Bs , Cs, Ds, Fs) Quantitative, placed in order, equal distance between attributes, and TRUE ZERO. Income (in terms of actual amount): people who earn $200 per week make twice as much as those earning $100 per week, but only half as much as those earning $400 per week. (Also possible to have $0 income.)

Levels of Measurement & Central Tendency Measures:

4 Levels of Measurement & Central Tendency Measures Nominal Ordinal Ratio Mode only Mode and Median only Mode , Median , Mean (and because of “true zero” can say that one attribute has a particular “ratio” to another attribute (people who earn $200 per week make twice as much as those earning $100 per week))

ratio level of measurement example:

ratio level of measurement example

PowerPoint Presentation:

Reported weekly income for SOC 1013 students: $125, $45, $200, $10, $200, $75, $10, $0, $100, $200, $100, $80, $150, $25, $100, $0, $100 Income 0 10 25 45 75 80 100 125 150 200 Frequency 2 2 1 1 1 1 4 1 1 3 17 % 11.8 11.8 5.9 5.9 5.9 5.9 23.5 5.9 5.9 17.6 100.1 Can you calculate the MEAN? THEN: Sum all incomes, then divide by total frequency (i.e., number of cases (N)). FIRST: Arrange attributes in order and then specify the frequency for each attribute. (To complete frequency distribution, it would also be of value to calculate percentage of attribute. Although this is not necessary for calculating mean.)

PowerPoint Presentation:

Reported weekly income for SOC 1013 students: $125, $45, $200, $10, $200, $75, $10, $0, $100, $200, $100, $80, $150, $25, $100, $0, $100 Income 0 10 25 45 75 80 100 125 150 200 Frequency 2 2 1 1 1 1 4 1 1 3 17 % 11.8 11.8 5.9 5.9 5.9 5.9 23.5 5.9 5.9 17.6 100.1 $ x Freq 0 20 25 45 75 80 400 125 150 600 1,520 / 17 = $89.41 MEAN = $89.41

PowerPoint Presentation:

Reported weekly income for SOC 1013 students: $125, $45, $200, $10, $200, $75, $10, $0, $100, $200, $100, $80, $150, $25, $100, $0, $100 Income 0 10 25 45 75 80 100 125 150 200 Frequency 2 2 1 1 1 1 4 1 1 3 17 % 11.8 11.8 5.9 5.9 5.9 5.9 23.5 5.9 5.9 17.6 100.1 Can you calculate the MEDIAN? After arranging values for all cases in order (ascending or descending), locate the mid-point value. HINT: There are 17 cases, so which case is the mid-point? The mid-point is the 9 th case. (BTW: where would be mid-point if there were 18 cases?) What is the value of the 9 th case? MEDIAN = $100

PowerPoint Presentation:

Reported weekly income for SOC 1013 students: $125, $45, $200, $10, $200, $75, $10, $0, $100, $200, $100, $80, $150, $25, $100, $0, $100 Income 0 10 25 45 75 80 100 125 150 200 Frequency 2 2 1 1 1 1 4 1 1 3 17 % 11.8 11.8 5.9 5.9 5.9 5.9 23.5 5.9 5.9 17.6 100.1 Can you calculate the MODE? HINT: Which value occurs most frequently? MODE = $100

Other Examples:

Other Examples

PowerPoint Presentation:

11 Responses to open-ended question: "What is your favorite type of ethnic food?"   Mexican - 50 Lebanese - 4 Soul food - 11 Chinese - 15 German - 3 Italian - 25 Greek - 2 Japanese - 3   Level of Measurement? _______________________________ Mean ______ Median ______ Mode ______ nominal not possible not possible Mexican

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12 Question asked of sample of San Antonio residents: "For next season, in which place will the Spurs finish the playoffs?"   first (championship) - 15 in playoffs, but eliminated prior to the finals - 8 second (lose in the finals) - 9 not make the playoffs - 1   Level of Measurement _______________________________ Mean ______ Median ______ Mode ______ ordinal not possible first second

PowerPoint Presentation:

13 Ten most frequently selected lottery numbers (painted on ping pong balls) during 2013, including their frequency of selection (in parenthesis):   23 (18), 33 (16), 42 (14), 18 (14), 49 (12), 22 (10), 44 (9), 3 (8), 29 (8), 8 (8) Level of Measurement _______________________________ Mean ______ Median ______ Mode ______ nominal (balls are simply differentiated on the basis of numerical symbol) not possible not possible 23

PowerPoint Presentation:

14 Responses to survey question asked to respondents : "How much money do you earn per hour at your current main job?"   $15.25 10.00 7.50 8.50 9.75 6.00 11.50 14.50 5.50 9.25 11.00 7.50 7.50 9.00 8.25   Level of Measurement _______________________________ Mean ______ Median ______ Mode ______ ratio $9.40 $9.00 $7.50

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