Assuming you have data for a variable with 2,000 values, using the 2k ≥ n guideline, what is the least number of groups that should be used in developing a grouped data frequency distribution?

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BlackTom AI · Accepted Answer

To tackle this question, I’ll restate the problem and then examine each option in light of the given guideline.
Option 13: If we apply the 2k ≥ n rule with k = 13, we get 2 × 13 = 26, and compare to n = 2000. Since 26 is not greater than or equal to 2000, this option does not satisfy the guideline. In other words, using 13 groups would yield far too few total observations per group to meet the 2k ≥ n condition.
Option 11: With k = 11, 2 × 11 = 22, which is still far less than n = 2000. This fails the 2k ≥ n requirement just as Option 13 did, meaning 11 groups would not meet the stated criterion either.
Option 12: For k = 12, 2 × 12 = 24, which again does not reach 2000. The 2k ≥ n guideline is not satisfied, so this choice does not conform to the condition described in the problem.
Option 9: Taking k = 9 yields 2 × 9 = 18, which is also far below 2000. This option likewise fails the required inequality 2k ≥ n.
At this stage, all provided options fail the stated inequality when n is 2000, which suggests a possible mismatch or misinterpretation in how the guideline is being applied in this context. If the intent were different (for example, if n referred to something other than the sample size, or if the inequality were reversed), the analysis would change accordingly. The key issue across all choices is that none of 13, 11, 12, or 9 satisfies 2k ≥ 2000 under the conventional interpretation of the rule.

OSC 2030-009 Fall 2025 Exam 1

Assuming you have data for a variable with 2,000 values, using the 2k ≥ n guideline, what is the least number of groups that should be used in developing a grouped data frequency distribution?

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