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You have been observing the local Democratic Party in a large city and have compiled some information about a small sample of party regulars. Find the appropriate measure of central tendency for each variable. Respondent Gender Social Class No. of Years Education Marital Status No. of Children A M High 32 High School Married 5 B M Middle 17 High School Married 0 C M Working 32 High School Single 0 D M Working 50 8 th grade Widowed 7 E M Working 25 4 th grade Married 4 F M Middle 25 High School Divorced 3 G F High 12 College Divorced 3 H F High 10 College Separated 2 I F Middle 21 College Married 1 J F Middle 33 College Married 5 K M Working 37 High School Single 0 L F Working 15 High School Divorced 0 M F Working 31 8 th grade Widowed 1

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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 3.3P
Textbook Problem
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You have been observing the local Democratic Party in a large city and have compiled some information about a small sample of party regulars. Find the appropriate measure of central tendency for each variable.

Respondent Gender Social Class No. of Years Education Marital Status No. of Children
A M High 32 High School Married 5
B M Middle 17 High School Married 0
C M Working 32 High School Single 0
D M Working 50 8th grade Widowed 7
E M Working 25 4th grade Married 4
F M Middle 25 High School Divorced 3
G F High 12 College Divorced 3
H F High 10 College Separated 2
I F Middle 21 College Married 1
J F Middle 33 College Married 5
K M Working 37 High School Single 0
L F Working 15 High School Divorced 0
M F Working 31 8th grade Widowed 1

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 six variables Gender, Social Class, No. of years in Party, Education, Marital Status, and No. of Children. Here, the variables No. of years in Party and No. of children have a numeric value; therefore, the level of measurement of these variables is interval-ratio. The variables Gender and Marital Status can be classified into categories; therefore, the level of measurement of these variables is Nominal. Further, the variable Social Class and 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 No. of years in Party, the measure of central tendency is: Mean

Formula Used:

The formula to calculate mean is given by,

X¯=i=1NXiN

The mean is given by,

X¯=i=1NXiN

Substitute 13 for N, 32 for X1, 17 for X2 and so on in the above mentioned formula,

X¯=32+17+...+15+3113=34013=26.15

For the variable No. of children, the measure of central tendency is: Mean

Formula Used:

The formula to calculate mean is given by,

X¯=i=1NXiN

The mean is given by,

X¯=i=1NXiN

Substitute 13 for N, 5 for X1, 0 for X2 and so on in the above mentioned formula,

X¯=5+0+...+0+113=3113=2.38

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

Formula used:

The Mode:

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

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