NDA2018MathematicsStatisticsActual
The standard deviation of the first N natural numbers can be obtained using which one of the following formulae?
Options
- A= N ^2-1 12
- B= N ^2-1 12
- C= N -1 12
- D= N ^2-1 6 ~N
Correct answer
B. = N ^2-1 12
Step-by-step solution
aligned & ^2= 1 N _ i=1 ^N X_i^2- ( 1 N _ i=1 ^N X_i )^2 = & 1 N (1^2+2^2+3^2+ .+ N ^2 )- ( 1 ~N (1+2+3+ .+ N ) )^2 = & 1 ~N ~N ( ~N +1)(2 ~N +1) 6 - ( 1 ~N ~N ( ~N +1) 2 )^2 = & N ^2-1 12 = N ^2-1 12 . aligned