Question

Consider the following statements in respect of the set $S=\{1,2,3,4,.......n\}$
1. $(n+1)/2$ is the median of the numbers is $S$.
2. $n$ is the mode of the numbers is/are correct?
A. 1 only
B.2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer 1

Hint: To solve this particular problem we need to know the basics about sets and median and mode of numbers, there are two statements given, we should go through each and analyze the validity of those statements separately.

Complete step-by-step answer:
In the first statement it is given that, $(n+1)/2$ is the median of the numbers $S$.
This statement is incorrect because it is not given that the given value of $n$ is odd or even and the provided equation in the statement is the formula of median of odd number of observations, so clearly the given first statement is wrong.

In the second statement it is given that, $n$ is the mode of the numbers in S.
This statement is incorrect because we know that the mode is referred to the most occurring value on the set of data, so clearly the second statement is wrong in this problem.
By this we can conclude that neither 1 nor 2 is the correct option for the particular given problem, So D option is the correct option for the given problem.
So, the correct answer is “Option D”.

Note: The problem can be solved by the above method, for that we need to have the knowledge of the formula for the median of even and odd numbers and we need to know about the meaning of mode and some basics about the sets.