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BITSAT2024MathematicsStatisticsActual

The mean of n items is X . If the first item is increased by 1 , second by 2 and so on, the new mean is :

Options

  1. AX + x 2
  2. BX +x
  3. CX + n +1 2
  4. DNone of these

Correct answer

C. X + n +1 2

Step-by-step solution

Let the items be a ₁, a ₂, . ., a _ n then X = a₁+a₂+ .+a_n n Now, according to the given condition: X = (a₁+1 )+ (a₂+2 )+ + (a_n+n ) n = X + 1+2+3+ +n n = X + n(n+1) 2 n (using sum of n natural nos.) = X + n +1 2 .

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