   Chapter 3, Problem 3.10P

Chapter
Section
Textbook Problem

SOC As the head of a social services agency, you believe that your staff of 20 social workers is very much overworked compared with 10 years ago. The case loads for each worker are reported below for each of the two years in question. Has the average caseload increased? Which measure of central tendency is most appropriate to answer this question? Why? 2002 2012 52 55 42 82 50 49 75 50 57 50 69 52 49 52 65 50 45 59 58 55 65 60 64 65 60 65 69 60 55 68 60 60 42 60 50 60 50 42 60 60

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, the variable Caseload has a numeric value; therefore, the level of measurement of this variable is interval-ratio.

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 Case load, the measure of central tendency is: Mean.

Formula Used:

The formula to calculate mean is given by,

X¯=i=1NXiN

For year 2002:

Substitute 20 for N, 52 for X1, 50 for X2 and so on in the above mentioned formula,

X¯=52+50+

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