Gini Index The Gini Index is a measure of how evenly income is distributed within a country, ranging from 0 to 100. An index of 0 suggests income is distributed with perfect equality. The higher the number, the worse the income inequality. The data below represent the Gini Index for a random sample of countries. Note: The United States has a Gini Index of 45 and Sweden has the lowest Gini Index. With a first class having a lower class limit of 20 and a class width of 5:

g. Does one frequency distribution provide a better summary of the data than the other? Explain.

Verified step by step guidance

1. Step 1: Understand the two frequency distributions being compared. One distribution uses class intervals starting at 20 with a class width of 5 (e.g., 20-24.9, 25-29.9, etc.), while the other distribution likely uses different class intervals or grouping methods. Identify the exact class intervals and frequencies for both distributions.
2. Step 2: Calculate the frequency for each class interval in both distributions by counting how many Gini Index values fall within each class. This will give you the frequency distribution tables for both methods.
3. Step 3: Analyze the shape and spread of each frequency distribution. Look for how well each distribution summarizes the data, considering factors such as the number of classes, the clarity of the distribution shape (e.g., skewness, modality), and how well the classes capture the variation in the data.
4. Step 4: Evaluate which frequency distribution provides a better summary by considering the balance between detail and simplicity. A better summary will have classes that are neither too broad (losing detail) nor too narrow (too many classes, making it complex), and it should clearly show the distribution pattern of the Gini Index values.
5. Step 5: Conclude by explaining which frequency distribution is more effective based on your analysis, supporting your reasoning with observations about the clarity, interpretability, and usefulness of the frequency tables in representing the income inequality data.

Key Concepts

Frequency Distribution

A frequency distribution organizes data into classes or intervals, showing how many data points fall into each class. It helps summarize large data sets by grouping values, making patterns like skewness or concentration easier to identify. Choosing appropriate class widths and limits is crucial for an informative distribution.

Gini Index

The Gini Index measures income inequality within a population, ranging from 0 (perfect equality) to 100 (maximum inequality). It provides a single value summarizing how income is distributed, useful for comparing countries or regions. Understanding its scale and interpretation is key to analyzing income data.

Comparing Frequency Distributions

When comparing frequency distributions, consider how well each summarizes the data's shape, spread, and key features. A better summary captures important details without oversimplifying or overcomplicating. Evaluating class width, number of classes, and clarity helps determine which distribution is more effective.