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For (2n + 1) observations $x_{1}, - x_{1}, x_{2}, - x_{2}, \dots, x_{n}, - x_{n}$ , and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true?

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SD < MD

SD > MD

SD = MD

Nothing can be said in general about the relationship between SD and MD

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detailed solution

Correct option is B

On arranging the given observations in ascending order, we getAll negative terms 0⏟(n+1)th term All positive termsMedian of given observations = (n + 1)th term = 0∴ SD>MD

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For (2n + 1) observations x1,−x1,x2,−x2,…,xn,−xn, and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true?

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

For (2n + 1) observations $x_{1}, - x_{1}, x_{2}, - x_{2}, \dots, x_{n}, - x_{n}$ , and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true?