Within Dixon's Range Statistic, what does R represent?

• A. The sum of all values
• B. The range of all values excluding the extreme
• C. The standard deviation of all values
• D. The range of all values including the extreme value

Answer: (D)

R in Dixon's Range Statistic is the range across the entire sample, from the smallest to the largest value, including the extreme values. It measures the total spread of the data and is used to gauge whether the most extreme observation is an outlier by comparing its gap from the rest to the overall range. For example, with data like 2, 4, 6, 100, the range including extremes is 100 minus 2 equals 98. A very large extreme value relative to this overall range suggests it may be an outlier. This is not the sum of values, not the standard deviation, and not the range that excludes the extremes.