Math, asked by BrainlyHelper, 1 year ago

The mean of n observation is X. If the first item is increased by 1, second by 2 and so on, then the new mean is
(a)X+n
(b)X+n/2
(c)X+(n+1)/2
(d)None of these

Answers

Answered by nikitasingh79
1

SOLUTION :  

The correct option is (c) : X + ((n +1)/2)

Let the n observations be x1, x2, x3 , ………...xn .  

Mean (X) =  (x1 + x2 +  x3 +…...xn) / n  

nX = x1 + x2 +  x3 +…...xn …………(1)

Given : First item is increased by 1 second by 2 and so on

New observations are (x1 + 1) ,  (x2 + 2),  x3 + 3) +……(xn + n) .

New Mean (X) =  (x1 +1) + (x2 + 2) +  (x3 +3 )+ ……(xn + n ) / n  

New mean  = (x1 + x2 +  x3 +…...xn) + (1 + 2 + 3 + ……..+ n ) /n  

New mean =[ nX +( n(n +1)/2)] / n   [from eq1 ]  

[The sum of the first n natural numbers : n(n +1)/2]

New mean = n[X + ((n +1) /2)] / n

Hence, the New mean is = X + ((n +1)/2)

HOPE THIS ANSWER WILL HELP YOU……

Answered by amangoyal23
2
correct option is (c).
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