If the mean deviation of the numbers 1,1+d,1+2d,⋅,1+100d from their mean is 255, then d is equal to:
10.1
Mean=101+d(1+2+3+⋯+100)101=1+d×100×101101×2=1+50d
∵ Mean deviation from the mean = 255
⇒1101[|1−(1+50d)|+|(1+d)−(1+50d)|+|(1+2d)−(1+50d)|+⋯+|(1+100d)−(1+50d)|]=255⇒2d[1+2+3+⋯+50]=101×255⇒2d×50×512=101×255⇒d=101×25550×51=10.1