Which of the following is least likely to be used as a criterion when choosing the number of bins ($n$ classes) in a frequency distribution?

• A. Choosing a number of bins that makes the distribution easy to interpret
• B. Selecting bins based on the alphabetical order of data values
• C. Making sure that the range of each bin is equal
• D. Ensuring that each bin has approximately the same number of data points

Answer: (B)

Verified step by step guidance

1. Understand that when choosing the number of bins (or classes) in a frequency distribution, the goal is to represent the data clearly and meaningfully.
2. Common criteria include: making the distribution easy to interpret, ensuring bins have equal ranges, and sometimes ensuring bins have approximately equal numbers of data points to balance the distribution.
3. Recognize that selecting bins based on the alphabetical order of data values is unrelated to the statistical properties of the data and does not help in meaningful data summarization.
4. Therefore, the least likely criterion to be used is the one that does not contribute to a meaningful or interpretable frequency distribution, which is selecting bins based on alphabetical order.
5. In summary, focus on criteria that improve interpretability and statistical relevance, rather than arbitrary or non-numeric ordering.