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Let x1, x2,…, x11 be 11 distinct positive integers. If we replace the largest of these integers by the median of the other 10 integers, then

(a) the median remains the same

(b) the mean increases

(c) the median decreases

(d) the mean remains the same

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Answer is : (c) the median decreases

Let the given 11 distinct positive integers are in increasing order

x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, so x11

is largest of these integers and the median is x6.

Now, median of first 10 numbers is

x6+x6/2 = m (Let)

Now, we have to replace largest number x11 by m and then increasing order will be

So, median decreases.

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