- Organize the 51 home ownership rates into predefined intervals of width 5 starting at 40.
- Count the number of observations within each interval to determine the frequency.
- Verify the total number of observations sums to 51.
- Fill the frequency distribution table with the values: \(\boxed{2, 2, 3, 4, 17, 19, 3, 1}\).
Explanation
- Understand the problem and data categorization
To construct the frequency distribution, we first identify the 51 home ownership rates. We have 51 data points ranging from 41.9% to 75%. We need to categorize these into the specified class intervals: 40-44.9, 45-49.9, 50-54.9, 55-59.9, 60-64.9, 65-69.9, 70-74.9, and 75-79.9.
- Categorize and count the frequencies
We carefully sort the rates and tally each data point into its corresponding class interval:
- 40-44.9: There are 2 rates (41.9, 44.0).
- 45-49.9: There are 2 rates (48.3, 45.4).
- 50-54.9: There are 3 rates (53.0, 53.2, 52.1).
- 55-59.9: There are 4 rates (56.6, 57.0, 55.0, 59.5).
- 60-64.9: There are 17 rates (61.6, 62.1, 63.2, 62.7, 60.7, 60.3, 63.5, 62.8, 61.6, 61.5, 64.1, 62.2, 62.3, 60.0, 62.0, 60.5, 60.4).
- 65-69.9: There are 19 rates (68.3, 65.2, 67.8, 66.8, 67.8, 65.5, 65.6, 66.0, 68.3, 65.5, 65.2, 65.0, 66.8, 65.6, 65.2, 69.1, 67.9, 67.0, 68.1).
- 70-74.9: There are 3 rates (71.3, 71.3, 71.3).
- 75-79.9: There is 1 rate (75.0).
Total frequency: \(2 + 2 + 3 + 4 + 17 + 19 + 3 + 1 = 51\). The sum confirms that all 51 regions are included.
- Construct the final frequency distribution table
Based on our counts, we can now complete the requested frequency table.
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Examples
Understanding frequency distributions is essential in real-world data analysis, such as when public policy experts evaluate socio-economic indicators across different states or regions. By grouping large datasets into classes, analysts can easily visualize the distribution of home ownership rates, identify the most common ranges, and detect outliers, helping them make more informed decisions about housing programs and regional support. For example, if a researcher wanted to compare the concentration of home ownership across different countries, they would use similar techniques to create a summary distribution to see where the majority of the data lies.