If a data set has 740 values that have been sorted from low to high, which value in the data set will be the 20th percentile?

Question

BlackTom AI · Accepted Answer

To determine the 20th percentile in a sorted data set, we need to identify the value below which 20% of the data fall.
First, compute 20% of the total count: 0.20 × 740 = 148.0. This suggests that the 20th percentile lies around the 148th position, but because 740 is a discrete set and percentile definitions can vary, some conventions place the percentile between specific positions rather than at a single index.
Option-by-option analysis:
- The 20th value: If we were using a simple rank-based approach where the percentile corresponds exactly to a single position, the 20th percentile would be the 148th value according to the 0.20 × n calculation. However, this ignores the fractional position that often arises in percentile definitions and can misrepresent the true cutoff point for 20% of data.
- The 148th value: This would align with a straightforward 0.20 × n calculation giving 148th position as the percentile point. Yet, because we typically want to account for the fact that 20% does not always align perfectly with a single data point, many standard methods use an interpolation between positions when the product 0.20 × n is not an integer.
- The average of the 148th and 149th values: This choice corresponds to the common interpolation-based percentile definition for data sets where the percentile falls between two adjacent data points. Since 0.20 × 740 = 148 exactly, some definitions still interpolate between 148th and 149th to capture the precise cutoff point in a way that reflects the surrounding data. In many instructional contexts, this averaged value is the standard answer for the 20th percentile when using a method that averages the bounding values around the percentile position.
- None of the above: This would be correct only if none of the above options matched the accepted definition for the percentile in use. Given that the averaged between the 148th and 149th is a recognized method for percentile calculation in this scenario, this option is not appropriate.
In summary, the most defensible choice here is that the 20th percentile is represented by the average of the 148th and 149th values, reflecting a percentile definition that uses interpolation between adjacent values when identifying cutoffs in a sorted data set.

OSC 2030-009 Fall 2025 SUBMIT: Graded Homework Module 2 (Chap 3)

If a data set has 740 values that have been sorted from low to high, which value in the data set will be the 20th percentile?

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