The mean of n observation is x. If the first observation is increased by 1, the second by 2, the third by 3, and so on, then the new mean is
(a)x+2n+1
(b)x+n+1/2
(c)x+n+1
(d)x-n+1/2
Answers
Answered by
3
SOLUTION :
The correct option is (b) : 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 observation 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
0
Answer:
According to problem:
a=1
d=2
∴S
n
=
2
n
[2a+(n−1)d]
=
2
n
[2+2n−2]
=n
2
∴Mean=
n
S
n
=
n
n
2
=n
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