Question

If the mean deviation of the number 1,1 + d,1 + 2d, ...... 1 + 100d from their mean
is 255 then the 'd' is equal to ............
​

Answer 1

Answer:

10.1

Step-by-step explanation:

Sₙ of an AP = n/2[2a + (n - 1)d]

The given series 1 , 1 + d, 1 + 2d, ........ 1 + 100d

Number of terms in the series = 101

Mean of this series = S₁₀₁ of [1  + 1 + d + 1 + 2d .....+ (1 + 100d)]/101.

Sum to 101 terms of series 1  + 1 + d + 1 + 2d .....+ (1 + 100d)

                                                     = S₁₀₁ =  101/2[2*1 + (101 - 1)d]

                                                    = 101 (1 + 50d)

=> Mean of the series = 101 (1 + 50d)/101 = 1 + 50d.

Therefore mean deviation from mean

=  1/101  *   101

                 ∑    (1 + rd) - (1 + 50d)

                r = 0

             =  2d/101 ( 50 * 51 /2)

=> 255 = 2d/101 ( 50*51/2)

=> 255 = 50 * 51 * d / 101

=> d = 255 * 101 / 50 * 51 = 10.1