Chapter 3, Problem 3.8P

BuyFind*arrow_forward*

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,

Substitute 30 for

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

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Applied Calculus

Calculus (MindTap Course List)

Precalculus: Mathematics for Calculus (Standalone Book)

Calculus: Early Transcendentals

Finite Mathematics and Applied Calculus (MindTap Course List)

Calculus: Early Transcendental Functions

Multivariable Calculus

Single Variable Calculus: Early Transcendentals, Volume I

Calculus: An Applied Approach (MindTap Course List)

Statistics for The Behavioral Sciences (MindTap Course List)

Calculus (MindTap Course List)

Understanding Basic Statistics

Probability and Statistics for Engineering and the Sciences

Single Variable Calculus

Finite Mathematics

Intermediate Algebra

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Elementary Geometry For College Students, 7e

Elements Of Modern Algebra

Mathematical Applications for the Management, Life, and Social Sciences

Contemporary Mathematics for Business & Consumers

Elementary Technical Mathematics

Mathematical Excursions (MindTap Course List)

Trigonometry (MindTap Course List)

Single Variable Calculus: Early Transcendentals

Calculus of a Single Variable

Calculus: Early Transcendental Functions (MindTap Course List)

Finite Mathematics for the Managerial, Life, and Social Sciences

Introduction To Statistics And Data Analysis

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Study Guide for Stewart's Multivariable Calculus, 8th

Elementary Geometry for College Students