Let x 1 , x 2 , … , x 11 be 11 distinct positive integers. If we replace the largest of these integers by the median of the other 10 integers, then

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Let x 1 , x 2 , &#8230; , x 11 be 11 distinct positive integers. If we replace the largest of these integers by the median of the other 10 integers, then

Quantrex Academy · Accepted Answer

Correct answer: D. the mean remains the same

Let the given 11 distinct positive integers are in increasing order x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x 8 , x 9 , x 10 , x 11 , so x 11 is largest of these integers and the median is x 6 . Now, median of first 10 numbers is x 6 + x 6 2 = m ( &#160;Let&#160; ) Now, we have to replace largest number x 11 by m and then increasing order will be x 1 , x 2 , x 3 , x 4 , x 5 , m , x 6 , x 7 , x 8 , x 9 , x 10 &#8757; &#160;&#160; m &#60; x 6 as x 5 &#60; x 5 + x 6 2 &#60; x 6 So, median decreases.

Let x 1 , x 2 , … , x 11 be 11 distinct positive integers. If we replace the largest of these integers by the median of the other 10 integers, then

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Let x 1 , x 2 , &#8230; , x 11 be 11 distinct positive integers. If we replace the largest of these integers by the median of the other 10 integers, then

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Correct answer

Step-by-step solution

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Let x 1 , x 2 , … , x 11 be 11 distinct positive integers. If we replace the largest of these integers by the median of the other 10 integers, then