UGC NET Questions (Paper – 1)

This option is correct because for n observations arranged in order, with n odd, the median is located at position (n+1)/2. This ensures that there are an equal number of observations on both sides of the median. The formula is standard in statistics for odd-sized data sets. Therefore, the median is at the ((n+1)/2)th position.

Option A:
Saying nth position would place the median at the last observation, which is the maximum value in an ascending list. This ignores the central nature of the median. Hence, nth position is not correct.

Option B:
The ((n+1)/2)th position ensures that the median lies exactly in the middle of the ordered list when n is odd. For example, if n = 5, the median is at position (5+1)/2 = 3, which has two values on each side. This matches the concept of a central value and so this option is correct.

Option C:
The (n/2)th position is only meaningful when n is even or when adjusted properly. For odd n, n/2 is not an integer and does not indicate a valid central index. Therefore, this option does not provide the correct position formula.

Option D:
The (n−1)th position lies near the end of the data and does not represent the middle. It would heavily bias toward higher values when the data are ordered ascending. Thus, this position is not the median location for an odd number of observations.