Answer the following. When calculations are required, remember to write down the

Question

Answer the following. When calculations are required, remember to write down the formula and to show all work.

1. Report all appropriate measures of central tendency for this distribution of ethnicity. (1 point)

63 White
16 Hispanic
12 African American
5 Asian
1 American Indian or Alaska Native 1 Other

2. Report all appropriate measures of central tendency for this distribution of religious affiliation. (1 point)

45 Protestants 21 Catholics 2 Jews
1 Muslim

2 Others
20 Unaffiliated.

3. Report all appropriate measures of central tendency for this distribution of strength of support for capital punishment. 1 stands for “strongly disagree”; 2 for “disagree”; 3 for “neutral”; 4 for “agree”; and 5 for “strongly agree.” (1 point)

{1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5}

4. Report all appropriate measures of central tendency for this distribution of time a group of students spent preparing for a final, measured in hours. (1 point)

{1, 2, 3, 3, 3, 4, 5, 5, 7, 10, 12}

Explanation / Answer

Q1: As this is a categorical variable with categories: white, hispanic, African American, Asian, American Indian, Alaska Native , therefore the appropriate measure of central tendency here would be the mode of the distribution. The mode is defined as the category with the highest frequency that is the white. Therefore white is the mode of the given distribution.

Q2: As this is a categorical variable with categories: Protestants, catholic, Jews, muslims, others, unaffiliated , therefore the appropriate measure of central tendency here would be the mode of the distribution. The mode is defined as the category with the highest frequency that is the white. Therefore Protestants is the mode of the given distribution.

Q3: This is a kind of an ordinal variable, where we can have order to the values. Here we can arrange the data in ascending order as: {1, 1, 1, 1, 2, 2, 4, 4, 4, 5, 5}. Now for this kind of a variable, median is the best choice for a central tendency. Here as we have got 11 values, therefore the middle value would be the 6th value. Therefore the median of the given distribution here is 2 that is disagree

Q4: Here the variable defined is the time a group of students spent preparing for a final, measured in hours, the central tendency here would be the mean as it a discrete numerical variable. For the given data: {1, 2, 3, 3, 3, 4, 5, 5, 7, 10, 12}, the mean is computed as: (1 + 2 + 3 + 3 + 3 + 4 + 5 + 5 + 7 + 10 + 12)/ 11 = 55/11 = 5

Therefore the mean of the distribution is 5 in this case.

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