When dealing with data collected using a qualitative, nominal variable such as drink sizes (small, medium, or large), you must consider the characteristics of nominal data. Here is a step-by-step explanation of what is true about a frequency table summarizing such data:
1. Qualitative Nominal Variables:
- These variables represent categories without a natural order or ranking. For example, drink sizes like small, medium, and large fall into different categories that don't have a numerical relationship.
2. Frequency Table:
- A frequency table for nominal variables lists the distinct categories and the count (frequency) of observations in each category.
3. Analysis of Options:
- The "2 to the k rule" can be applied:
- This rule helps determine the number of bins/classes when dealing with quantitative data to create histograms or frequency distributions. It is not applicable to nominal data.
- The upper and lower class limits must be calculated:
- This concept applies to quantitative data, where numerical ranges define the classes. Nominal data categories like small, medium, and large don't have numerical range limits.
- The number of classes corresponds to the number of a variable's values:
- This is true. For qualitative, nominal variables, each distinct value (category) is a separate class. If the nominal variable has values small, medium, and large, there are precisely three categories or classes.
- Class midpoints can be computed:
- Class midpoints are relevant for quantitative data when calculating the center of classes. Since nominal data categories don’t have inherent numerical relationships, midpoints cannot be computed.
4. Conclusion:
- For qualitative, nominal data, the number of classes in a frequency table directly corresponds to the number of distinct values (categories) of the variable.
Thus, the correct option is:
The number of classes corresponds to the number of a variable's values.
