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The mean of $n$ observations is $\bar{x}$ , 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

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\bar{x} + (2 n + 1)

\bar{x} + (\frac{n + 1}{2})

\bar{x} + (n + 1)

\bar{x} - (\frac{n + 1}{2})

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detailed solution

Correct option is B

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

$\frac{sum of " n "observation}{Number of observatin} = \bar{x}$

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

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

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

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

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

$= \frac{sum of " n "observatin}{n} + \frac{\frac{n (n + 1)}{2}}{n}$

$= \bar{x} + (\frac{n + 1}{2})$

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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