A variety of information has been collected for all district high schools. Find the most appropriate measure of central tendency for each variable, and summarize this information in a paragraph. (HINT: The level of measurement of the variable will generally tell you which measure of central tendency is appropriate. Remember to organize the scores from high to low before finding the median.) High School Enrollment Largest Racial/Ethnic Group % College Bound Most Popular Sport Condition of Physical Plant (10 = Excellent) A 1400 White 25 Football 10 B 1223 White 77 Baseball 7 C 876 Black 52 Football 5 D 1567 Hispanic 29 Football 8 E 778 White 43 Basketball 4 F 1690 Black 35 Basketball 5 G 1250 White 66 Soccer 6 H 970 White 54 Football 9

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 3.2P
Textbook Problem
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A variety of information has been collected for all district high schools. Find the most appropriate measure of central tendency for each variable, and summarize this information in a paragraph. (HINT: The level of measurement of the variable will generally tell you which measure of central tendency is appropriate. Remember to organize the scores from high to low before finding the median.) High School Enrollment Largest Racial/Ethnic Group % College Bound Most Popular Sport Condition of Physical Plant (10 = Excellent) A 1400 White 25 Football 10 B 1223 White 77 Baseball 7 C 876 Black 52 Football 5 D 1567 Hispanic 29 Football 8 E 778 White 43 Basketball 4 F 1690 Black 35 Basketball 5 G 1250 White 66 Soccer 6 H 970 White 54 Football 9

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 five variables Enrollment, Largest Racial/Ethnic Group, % College Bound, Most popular Sport, and Condition of Physical plant. Here, the variables Enrollment and % College Bound have a numeric value; therefore, the level of measurement of these variables is interval-ratio. The variables Largest Racial/Ethnic Group and Most Popular sport can be classified into categories. Therefore, the level of measurement of these variables is Nominal. Further, the variable Condition of physical plant 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 Enrollment, 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 8 for N, 1400 for X1, 1223 for X2 and so on in the above mentioned formula,

X¯=1400+1223+876+1567+778+1690+1250+9708=97548=1219.25

For the variable Largest Racial/Ethnic Group, 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: “White” occurs for most frequently. Therefore, the mode is “White”.

For the variable % College Bound, the measure of central tendency is: Mean

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