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NDA 2025 Maths · Mathematics · Statistics · easy

The mean of the first n natural numbers is (n+1)/(2). 2. The median of a data set is always one of the observations.

Single correct option

Consider the following statements:
1. The mean of the first nn natural numbers is n+12\dfrac{n+1}{2}.
2. The median of a data set is always one of the observations.
Which of the statements given above is/are correct?
  1. A. 11 only
  2. B. 22 only
  3. C. Both 11 and 22
  4. D. Neither 11 nor 22
Show answer and solution

Answer: (A) 11 only

The sum of the first nn natural numbers is n(n+1)2\frac{n(n+1)}{2}, so the mean is n+12\frac{n+1}{2}: statement 1 is correct. For an even number of observations the median is the average of the two middle values, such as 2.52.5 for 1,2,3,41,2,3,4, which is not an observation. Statement 2 is false.
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Original question written in the NDA 2025 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake