Q3 observation position in a sorted data set.

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

Answer: (D)

The third quartile is the 75th percentile—the value in a sorted list below which 75% of the data fall. When you index positions from 1 to n, a common way to place quartiles uses the ranks (n+1)/4, (n+1)/2, and 3(n+1)/4. The third quartile, therefore, sits at 3(n+1)/4. That rank (or position) identifies where you look in the ordered data to find Q3. Since this position may not be an exact integer, you typically interpolate between the neighboring observations to get the actual value, which aligns with the idea that 75% of data are at or below that point. For instance, with n = 8, the rank is 6.75, so Q3 lies between the 6th and 7th observations. This is why the correct position is 3(n+1)/4.