Given a frequency distribution of response times grouped into intervals, which interval accounts for the lowest percentage of response times?

• A. The interval with the largest $\mathrm{cumulative} \mathrm{frequency}$
• B. The interval with the smallest $\mathrm{relative} \mathrm{frequency}$
• C. The interval with the highest $\mathrm{midpoint} \mathrm{value}$
• D. The interval with the greatest $\mathrm{class} \mathrm{width}$

Answer: (B)

Verified step by step guidance

1. Understand the meaning of each option in the context of a frequency distribution: the interval with the largest cumulative frequency means the interval up to which the total frequency is highest; the interval with the smallest relative frequency means the interval with the lowest proportion of observations; the interval with the highest midpoint value refers to the interval whose midpoint (average of class boundaries) is the largest; the interval with the greatest class width refers to the interval that covers the largest range of values.
2. Recall that the percentage of response times in an interval is directly related to the relative frequency of that interval, which is calculated as the frequency of that interval divided by the total number of observations.
3. Identify that the interval accounting for the lowest percentage of response times is the one with the smallest relative frequency, because relative frequency represents the proportion of data points in that interval.
4. Note that cumulative frequency and midpoint values do not directly indicate the percentage of response times in a single interval; cumulative frequency accumulates frequencies up to that interval, and midpoint is just a representative value of the interval.
5. Conclude that to find the interval with the lowest percentage of response times, you should look for the interval with the smallest relative frequency.