JEE Main2016MathematicsStatisticsActual
If the mean deviation of the numbers 1 , 1 + d , … , 1 + 100 d from their mean is 255 , then a value of d is :
Options
- A10 . 1
- B5 . 05
- C20 . 2
- D10
Correct answer
A. 10 . 1
Step-by-step solution
Mean x - = 1 101 1 + 1 + d + 1 + 2 d … . 1 + 100 d = 1 101   × 101 2   1 + 1 + 100 d = 1 + 50 d Mean deviation from mean = 1 101 1 - 1 + 50 d + 1 + d - 1 + 50 d … . 1 + 100 d - 1 + 50 d = 2 d 101   1 + 2 + 3 … . + 50 = 2 d 101   50   50 + 1 2 = 2550 101 d = 255   ⇒ d = 10 .1