The mean of  n  observations is x¯ , if the first observation is increased by 1, the second observation by 2, the third observation 3 and so on, then the new mean is

# The mean of  $n$ observations is $\overline{x}$, if the first observation is increased by 1, the second observation by 2, the third observation 3 and so on, then the new mean is

1. A
$\overline{x}+\left(2n+1\right)$
2. B
$\overline{x}+\left(\frac{n+1}{2}\right)$
3. C
$\overline{x}+\left(n+1\right)$
4. D
$\overline{x}-\left(\frac{n+1}{2}\right)$

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### Solution:

Mean of  $"n"$  observations$=\overline{x}$

Sum of $"n"$ observation $=n\overline{x}$

After Add 1 to the 1st her , 2 to the 2nd here …$n$  to the ${n}^{th}$  term

Sum of observations $=$  Sum of  $"n"$ observation $+1+2+3+\cdots +n$

$=$  sum of $"n"$ observation $+\frac{n\left(n+1\right)}{2}$

$\therefore$ Mean $=$

$=\overline{x}+\left(\frac{n+1}{2}\right)$

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