Sullivan Survey Choose any quantitative variable from the SullivanStatsSurveyI at www.pearsonhighered.com/sollivanstats. Now choose a qualitative variable, such as gender or political philosophy. Determine the range and standard deviation by the qualitative variable chosen. For example, if you chose gender as the qualitative variable, determine the range and standard deviation by gender. Does there appear to be any difference in the measure of dispersion for each level of the qualitative variable?

Verified step by step guidance

1. Identify and select one quantitative variable from the SullivanStatsSurveyI dataset. This variable should be numerical, such as age, income, or hours worked.
2. Choose one qualitative variable from the dataset, such as gender, political philosophy, or any categorical variable that divides the data into groups.
3. Separate the data into groups based on the levels of the qualitative variable. For example, if you chose gender, create one group for males and another for females.
4. For each group, calculate the range and standard deviation of the quantitative variable. The range is calculated as \(\text{Range} = \text{Maximum value} - \text{Minimum value}\), and the standard deviation is calculated using the formula \(s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}\), where \(n\) is the number of observations in the group, \(x_i\) are the data points, and \(\bar{x}\) is the group mean.
5. Compare the calculated ranges and standard deviations across the groups to determine if there is a noticeable difference in the measure of dispersion for each level of the qualitative variable.

Key Concepts

Quantitative and Qualitative Variables

Quantitative variables represent numerical data that can be measured or counted, such as height or test scores. Qualitative variables describe categories or groups, like gender or political affiliation. Understanding the difference is essential for analyzing data by groups and comparing numerical summaries across categories.

Measures of Dispersion: Range and Standard Deviation

Range is the difference between the maximum and minimum values in a dataset, showing the spread of data. Standard deviation quantifies the average distance of data points from the mean, indicating variability. Both measures help assess how spread out the data are within each group defined by the qualitative variable.

Comparing Dispersion Across Groups

When data are divided by a qualitative variable, comparing measures of dispersion like range and standard deviation reveals differences in variability between groups. This comparison helps identify whether one group has more consistent or more varied data than another, providing insights into group characteristics.