AP EAMCET202021 Sep 2020Evening ShiftMathematicsStatisticsActual
The mean deviation from the mean of the series ((a),(a+d),(a+2 d), . .,(a+2 n d) ) is
Options
- A( n(n-1) d 2 n+1 )
- B( n(n+1) d 2 n+1 )
- C((n(n+1) d) )
- D( n(n+1) d 2 n )
Correct answer
B. ( n(n+1) d 2 n+1 )
Step-by-step solution
The mean of given series (a, a+d, a+2 d, , a+2 n d ) is ( 2 n+1 2 [2 a+(2 n) d] 2 n+1 =(a+n d)=m ) (let) So, the mean deviation (= 1 2 n+1 _ i=1 ^ 2 n+1 |x_i-m | ) ( aligned & = 1 2 n+1 [|n d|+|n d-d|+|n d-2 d|+ .+|n d-2 n d|] & = 2 d 2 n+1 [n+(n-1)+(n-2)+ .+1]= n(n+1) d 2 n+1 aligned ) Hence, option (b) is correct