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You have compiled the following information on each of the graduates voted “most likely to succeed” by a local high school for a 10-year period. For each variable, find the appropriate measure of central tendency. Case Present Income ($) Marital Status Owns a Home? Years of Education Post-High School A 104,000 Divorced Yes 8 B 68,000 Divorced No 4 C 54,000 Married Yes 4 D 45,000 Married No 4 E 40,000 Single No 4 F 85,000 Separated Yes 8 G 30,000 Married No 3 H 27,000 Married No 1 I 93,000 Married Yes 6 J 48,000 Single Yes 4

BuyFind

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 3.14P
Textbook Problem
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You have compiled the following information on each of the graduates voted “most likely to succeed” by a local high school for a 10-year period. For each variable, find the appropriate measure of central tendency.

Case Present Income ($) Marital Status Owns a Home? Years of Education Post-High School
A 104,000 Divorced Yes 8
B 68,000 Divorced No 4
C 54,000 Married Yes 4
D 45,000 Married No 4
E 40,000 Single No 4
F 85,000 Separated Yes 8
G 30,000 Married No 3
H 27,000 Married No 1
I 93,000 Married Yes 6
J 48,000 Single Yes 4

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 four variables Present Income ($), Marital Status, Owns a Home?, and Years of Education Post-High School. Here, the variable Present Income has a numeric value; therefore, the level of measurement of this variable is interval-ratio. The variables Marital Status and Owns a Home? can be classified into categories; therefore, the level of measurement of these variables is Nominal. Further, the variable Years of Education Post-High School 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 Present Income, the measure of central tendency is: Mean

Formula Used:

The formula to calculate mean is given by,

X¯=i=1NXiN

Substitute 10 for N, 104, 000 for X1, 68, 000 for X2 and so on in the above mentioned formula,

X¯=104,000+68,000+...+93,000+48,00010=59400010=59400

For the variable Marital Status, 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.

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

For the variable Owns a Home?, 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: “Yes” and “No” occurs for most frequently. Therefore, the mode is “Yes” and “No”.

For the variable Years of Education Post-High School, the measure of central tendency is: Median.

Arrange the data in the increasing order.

The data in increasing order is given by,

1 3 4 4 4 4 4 6 8 8

The number of terms is 10, which is even

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