Question

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.

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?

Answer 1

Since the dataset is not available, I will try to address this problem from a methodology point of view as understanding the methodology will help you answer the questions.

Report the mean, median, and mode.

If you are using SPSS, then you need to check the mean, median and mode boxes in the Frequencies tab, for the appropriate columns, in R we can use the mean(), median() and mode() functions directly

What might be the better measure for central tendency? (i.e., mean, median, or mode) and why?

The better measure ofcentral tendency is the median, as it is the midpoint of the dataset arranged in ascending order. It will not skewed by extreme values or outliers, like in the case of mean

Report the standard deviation.

Again the Std. Dev can be calculated using the sd() function in R by passing the appropriate column as input and by checking the std. dev. box in the appropriate tab in SPSS

How variable are the data?

This can be checked by checking the Std. Dev and variance of the dataset which will give a measure of the variation, while the mean, median and mode will give an idea of the skewness of the data