If the mean deviation of the numbers 1, 1+d, , 1+100d from their mean is 255, then a value of d is :

JEE Main 2016 Mathematics question

If the mean deviation of the numbers 1, , , from their mean is 255, then a value of is :

(1)Correct
(2)
(3)
(4)10

Answer: (1)

Solution

The 101 numbers form an arithmetic progression, so their mean is the middle term, . The deviation of the th term from this mean is , and the mean deviation is

MD = |k-50

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Question ID VK-115570