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AP EAMCET202017 Sep 2020Evening ShiftMathematicsStatisticsActual

The mean deviation about the mean of the set of first ' (n ) ' natural numbers, when ' (n ) ' is an even number is equal to

Options

  1. A(n )
  2. B( n 2 )
  3. C( n 3 )
  4. D( n 4 )

Correct answer

D. ( n 4 )

Step-by-step solution

Mean ( x = 1+2+ . n n = n(n+1) 2 n = n+1 2 ) Here, (n= ) even number Now mean deviation is ( aligned & M . D( x )= [ |1- n+1 2 |+ |2- n+1 2 | + .+ |n- n+1 2 | ] 1 n &= 2 n 1+2+ .+ ( n 2 ) n 2 terms &= 2 n [ n 2 ( n 2 -1+1 ) 2 ]= n 4 aligned )

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