SATHEE: Quantitative Aptitude Ques 2103

Quantitative Aptitude Ques 2103

Question: The mean of n observations is $ {{\bar{x}}_1}. $ If the first observation is increased by 1, second by 2 and so on, then their mean is $ {{\bar{x}}_2}. $ The value of $ {{\bar{x}}_2}-{{\bar{x}}_1} $ is [Oriental Insurance Company (AAO) 2012]

Options:

A) $ n $

B) $ \frac{n}{2}+1 $

C) $ \frac{n(n+1)}{2} $

D) $ \frac{(n+1)}{2} $

E) None of these

Show Answer

Answer:

Correct Answer: D

Solution:

Here, new mean, $ {{\bar{x}}_2} $ $ =\frac{x _1+x _2+…+x _{n}}{n}+\frac{1+2+3+…+n}{n} $ $ ={{\bar{x}}_1}+\frac{n(n+1)}{2n}={{\bar{x}}_1}=\frac{n+1}{2} $

$ \therefore $ $ {{\bar{x}}_2}+{{\bar{x}}_1}={{\bar{x}}_1}+\frac{n+1}{2}-{{\bar{x}}_1}=\frac{n+1}{2} $

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Quantitative Aptitude Ques 2103

Question: The mean of n observations is $ {{\bar{x}}_1}. $ If the first observation is increased by 1, second by 2 and so on, then their mean is $ {{\bar{x}}_2}. $ The value of $ {{\bar{x}}_2}-{{\bar{x}}_1} $ is [Oriental Insurance Company (AAO) 2012]

Options:

Answer:

Solution:

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