Q1 observation position in a sorted data set

Q1 observation position in a sorted data set

• A. n/2 th observation
• B. (n+1)/4 th observation
• C. 2(n+1)/4 th observation
• D. (n+3)/4 th observation

Answer: (B)

Quartiles split data into four equal parts, so the first quartile represents the 25th percentile. In an ordered list of n observations, the rank that corresponds to the 25th percentile is (n+1)/4. This position is derived from placing one-quarter of the data at or below that point, and, when n isn’t divisible by 4, you interpolate between neighboring observations to estimate Q1. The other expressions point to different ideas: n/2 and (n+1)/2 give the median position, not the first quartile, while (n+3)/4 reflects a less common convention. Therefore, (n+1)/4 is the standard position for the first quartile, making it the best choice. For example, if n = 16, the first quartile is around position (16+1)/4 = 4.25, so you interpolate between the 4th and 5th values.

Quartiles split data into four equal parts, so the first quartile represents the 25th percentile. In an ordered list of n observations, the rank that corresponds to the 25th percentile is (n+1)/4. This position is derived from placing one-quarter of the data at or below that point, and, when n isn’t divisible by 4, you interpolate between neighboring observations to estimate Q1.

The other expressions point to different ideas: n/2 and (n+1)/2 give the median position, not the first quartile, while (n+3)/4 reflects a less common convention. Therefore, (n+1)/4 is the standard position for the first quartile, making it the best choice. For example, if n = 16, the first quartile is around position (16+1)/4 = 4.25, so you interpolate between the 4th and 5th values.