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# Understanding Central Tendency and Variability

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List and fully describe the three measures of central tendency and the two measures of variability. Provide a social work example throughout your discussion post.

https://brainmass.com/sociology/research-methods/understanding-central-tendency-and-variability-603009

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The Three Measures of Central Tendency

The following are the statistical measures in which each play a different role in determining where the center of the distribution or the average score lies (Dr. Christopher L. Heffner, http://allpsych.com/researchmethods/centraltendency/#.VSNI9RPF8YI). I have referred to Dr. Heffner throughout this response because he provides an accurate and quick reference to your request.

Dr. Heffner provides a good synopsis of these measures.

1. Mean: The Statistical Average (also known as the arithmetic average)

All of the scores are added together and the sum is then divided by the total number of scores.

This measure is used more frequently; however, it is susceptible to extreme scores.

Example provided by Dr. Heffner:
If scores '8', '9', and '10' were added together and divided by 3
The mean would equal '9'

To make it an extreme score,
If '10' were changed to '100'
The mean of '8', '9', and '100' would be '39'

2. Median: The Middle Most Occurring Score when values are arranged in ascending or descending order

The median divides the distributions in half (50% of the numbers are on ...

#### Solution Summary

This solution will assist the student in understanding the measures of central tendency and the measures of variability within the scope of social work.

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## AIU case study: examine qualitative and quantitative data and write a professional report

The data set for our course is a sample of a survey conducted on the population of the American Intellectual Union (AIU). It is available via the following link: DataSet with DataSet Key which contains the following nine sections of data that will be used throughout our course:

(1) Gender (2) Age (3) Department (4) Position (5) Tenure (6) Overall Job Satisfaction (7) Intrinsic Job Satisfaction - Satisfaction with the actual performance of the job (8) Extrinsic Job Satisfaction- Things external to the job, e.g., office location, your work colleagues, your own office (cubicle/hard walled office, etc), and (9) Benefits - Health insurance, pension plan, vacation, sick days, etc.

American Intellectual Union (AIU) has assembled a team of researchers in the United States and around the world to study job satisfaction. Congratulations, you have been selected to participate in this massive global undertaking.

The study will require that you examine data, analyze the results, and share the results with groups of other researchers. Job Satisfaction is important to companies large and small and understanding it provides managers with insights into human behavior that can be used to strengthen the company's bottom line.

You will need to examine two of the nine sections of data, one section of qualitative data and one section of quantitative data, from the provided Unit 1 data set. Each section should include all data points. After analyzing your data, it will be necessary to write up a professional report. The requirements include providing the data you selected, discussing why the data was selected and what was learned by examining these sets of data. Your analysis should include using Excel to obtain information about the data through the use of three measures of central tendency (mean, median, mode) and the use of two measures of variability (standard deviation and variance). Some measures are appropriate for qualitative data and some are appropriate for quantitative data. If a measure is not applicable, then explain why. You will have to also provide 1 chart/graph for each of the results of the two processed sections of data (2 total), such as a pie or bar chart or a histogram. (A table is NOT a chart/graph.) Ensure that you label the chart/graph clearly. You will then need to discuss what you additionally learned from the results of this process. Explain why charts/graphs are important in conveying information in a visual format and why standard deviation and variation are important. Finally, you will need to combine all of the items above into one comprehensive report.

An Introduction
The data selected
Discussion (Why you selected your data and what you learned by examining your selected data set.)
The measures of central tendency and variability. (Copy and paste from your Excel process.)
The charts/graphs
Summary (what you learned and why the processes are important.)

(please note that all 29 observations for each variable selcted are to be used in the assignment)

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