Statistics Sequences Series

If the mean deviation about the median of the numbers a, 2a, ..., 50a is 50, then |a| equals

  1. 2
  2. 3
  3. 4
  4. 5

Answer

Median = 25.5a

Mean deviation about median = 50

∑|xi - 25.5a|/50 = 50

24.5a + 23.5a + . . + 0.5a + 0.5a + . . + 24.5a = 250

a + 3a + 5a + . . + 49a = 2500

25/2(50a) = 2500

The correct option is C.