# Discussion: Central Tendency and Variability

Understanding descriptive statistics and their variability is a fundamental aspect of statistical analysis. On their own, descriptive statistics tell us how frequently an observation occurs, what is considered “average”, and how far data in our sample deviate from being “average.” With descriptive statistics, we are able to provide a summary of characteristics from both large and small datasets. In addition to the valuable information they provide on their own, measures of central tendency and variability become important components in many of the statistical tests that we will cover. Therefore, we can think about central tendency and variability as the cornerstone to the quantitative structure we are building.

For this Discussion, you will examine central tendency and variability based on two separate variables. You will also explore the implications for positive social change based on the results of the data.

To prepare for this Discussion:

• Review this week’s Learning Resources and the Descriptive Statistics media program.
• For additional support, review the Skill Builder: Visual Displays for Categorical Variables and the Skill Builder: Visual Displays for Continuous Variables, which you can find by navigating back to your Blackboard Course Home Page. From there, locate the Skill Builder link in the left navigation pane.
• Review the Chapter 4 of the Wagner text and the examples in the SPSS software related to central tendency and variability.
• From the General Social Survey dataset found in this week’s Learning Resources, use the SPSS software and choose one continuous and one categorical variable Note: this dataset will be different from your Assignment dataset).
• As you review, consider the implications for positive social change based on the results of your data.
• Post, present, and report a descriptive analysis for your variables, specifically noting the following:For your continuous variable:
1. Report the mean, median, and mode.
2. What might be the better measure for central tendency? (i.e., mean, median, or mode) and why?
3. Report the standard deviation.
4. How variable are the data?
5. How would you describe this data?
6. What sort of research question would this variable help answer that might inform social change?

Post the following information for your categorical variable:

1. A frequency distribution.
2. An appropriate measure of variation.
3. How variable are the data?
4. How would you describe this data?
5. What sort of research question would this variable help answer that might inform social change?
• Frankfort-Nachmias, C., & Leon-Guerrero, A. (2018). Social statistics for a diverse society (8th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 3, “Measures of Central Tendency” (pp. 63-93)
• Chapter 4, “Measures of Variability” (pp. 94-127)

Wagner, W. E. (2016). Using IBM® SPSS® statistics for research methods and social science statistics (6th ed.). Thousand Oaks, CA: Sage Publications.

• Chapter 4, “Organization and Presentation of Information”
• Chapter 11, “Editing Output”

#### DATASETS

Document: Data Set 2014 General Social Survey (dataset file)Use this dataset to complete this week’s Discussion.Note: You will need the SPSS software to open this dataset.

Document: Data Set Afrobarometer (dataset file)Use this dataset to complete this week’s Assignment.Note: You will need the SPSS software to open this dataset.

Document: High School Longitudinal Study 2009 Dataset (dataset file)Use this dataset to complete this week’s Assignment.Note: You will need the SPSS software to open this dataset.

#### REQUIRED MEDIA

Laureate Education (Producer). (2016d). Descriptive statistics [Video file]. Baltimore, MD: Author.Note: The approximate length of this media piece is 7 minutes.In this media program, Dr. Matt Jones demonstrates the procedures used for central tendency and variability using SPSS software. Focus on how this demonstration might support your analysis in this week’s Assignment.