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Essentials Of Statistics

4th Edition
HEALEY + 1 other
ISBN: 9781305093836

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BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
ISBN: 9781305093836
Textbook Problem

SOC The accompanying table gives scores on four variables for 30 cases from the General Social Survey:

• “Age” is reported in years.

• “Happiness” consists of answers to the question “Taken all together, would you say that you are

1. Very happy

2. Pretty happy

3. Not too happy?”

• “Number of Partners” refers to sex partners over the past five years:

• A score of 0 to 4 is the actual number of partners.

• A score of 5 means 5–10 partners.

• A score of 6 means 11–20 partners.

• A score of 7 means 21–100 partners.

• A score of 8 means more than 100 partners.

• “Religion” is self-identified religious affiliation (Protestant, Catholic, Jew, Other, or None).

For each variable, find the appropriate measure of central tendency, and write a sentence reporting this statistical information as you would in a research report.

Respondent Age Happiness Number of Partners Religion
1 20 1 2 Protestant
2 32 1 1 Protestant
3 31 1 1 Catholic
4 34 2 5 Protestant
5 34 2 3 Protestant
6 31 3 0 Jew
7 35 1 4 None
8 42 1 3 Protestant
9 48 1 1 Catholic
10 27 2 1 None
11 41 1 1 Protestant
12 42 2 0 Other
13 29 1 8 None
14 28 1 1 Jew
15 47 2 1 Protestant
16 69 2 2 Catholic
17 44 1 4 Other
18 21 3 1 Protestant
19 33 2 1 None
20 56 1 2 Protestant
21 73 2 0 Catholic
22 31 1 1 Catholic
23 53 2 3 None
24 78 1 0 Protestant
25 47 2 3 Protestant
26 88 3 0 Catholic
27 43 1 2 Protestant
28 24 1 1 None
29 24 2 3 None
30 60 1 1 Protestant

To determine

To find:

The most appropriate measures of central tendency for each variable

Explanation

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 Age, Happiness, Number of Partners, and Religion. Here, the variable Age has a numeric value; therefore, the level of measurement of this variable is interval-ratio. The variables Number of Partners and Religion can be classified into categories; therefore, the level of measurement of these variables is Nominal. Further, the variable Happiness 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 30 for N, 20 for X1, 32 for X2 and so on in the above mentioned formula,

X¯=45+48+...+25+2315=126530=42.17

For the variable Number of Partners, 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.

In the data: “1” occurs for most frequently. Therefore, the mode is “1”.

For the variable Religion, 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.

In the data: “Protestant” occurs for most frequently. Therefore, the mode is “Protestant”.

For the variable,Happiness, the measures of central tendency is: Median.

Arrange the data in the increasing order.

The data in increasing order is given by,

1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
2
3
3
3

The number of terms is 30, which is even

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