When comparing two frequency distributions that summarize the same dataset, which of the following criteria best determines if one provides a better summary than the other?

• A. The distribution with the smallest $\mathrm{range}$ of values is always the best summary.
• B. The distribution that clearly displays the shape, central tendency, and variability of the data without excessive detail provides a better summary.
• C. The distribution that uses more class intervals, regardless of data spread, always provides a better summary.
• D. The distribution that has the most classes with zero $\mathrm{frequency}$ is preferred.

Answer: (B)

Verified step by step guidance

1. Understand that when comparing two frequency distributions summarizing the same dataset, the goal is to find which one best represents the data's key characteristics clearly and effectively.
2. Recall the main features a good frequency distribution should display: the shape of the data (distribution pattern), central tendency (such as mean or median), and variability (spread or dispersion).
3. Recognize that a distribution with too few classes may oversimplify the data, hiding important details, while one with too many classes may overcomplicate the summary with excessive detail and empty classes.
4. Evaluate the options by considering that the best summary balances detail and clarity, showing the essential features without unnecessary complexity or empty classes.
5. Conclude that the best frequency distribution is the one that clearly displays the shape, central tendency, and variability of the data without excessive detail, rather than simply having the smallest range, the most classes, or many zero-frequency classes.