There are 27 numbers in the list: 3x,6x,9x,...,81x. Because there are an odd number of numbers, the median is the 14‌th ‌ number in the list. Each number increases by 3x, so the 14‌th ‌ number is: 3x+(14−1)×3x=3x+39x=42x So, the median is 42x. The mean deviation about the median means we find the average of the distances from each value to 42x : ‌
|3x−42x|+|6x−42x|+...+|81x−42x|
27
=91 So, |3x−42x|+|6x−42x|+...+|81x−42x|=27×91 Every term inside the absolute value is a multiple of |x|. The differences |3x−42x|,|6x−42x|,...,|81x−42x| will be |39x|,|36x|,...,|0x|,...,|39x|. So the total sum is: |x|×(39+36+...+0+3+6+...+39)=27×91 The numbers in the bracket add up to 546 , so: |x|×546=27×91 |x|=‌