The median of the following observation is : 37, 31, 42, 43, 46, 25, 39, 43, 32

Median is the middle value of an ordered data set, so the first step is always to sort. Sorted, the nine observations are 25, 31, 32, 37, 39, 42, 43, 43, 46. With n = 9 (odd), the median is the (n+1)/2 = 5th value, which is 39. Option C is correct.

Why the others fail:

• A) 37 is the 4th value in the sorted list, one place short of the middle. It is often picked by someone who counts only partway.
• B) 38 is the average of 37 and 39. That method is used only when n is even, which it isn't here.
• D) 41 is not a value in the data and lies above the middle. The mean is about 37.6, so 41 is not a measure of central tendency for this set either.

Core concept: measures of central tendency (mean, median, mode) and how each responds to the data. Median is positional, so it is robust to extreme values such as 25 and 46. This matters in Mains when you discuss why median income or median age is preferred over mean in skewed distributions.

Trap: Skipping the sorting step, or averaging two middle values when n is odd.