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  • Let and M.D. be the mean and the mean deviation about <img alt="\bar{X}" src="http://

Let \bar{X} and M.D. be the mean and the mean deviation about \bar{X} of n observations   \large x_{i},i=1,2,.................,n.  If each of the observations is increased by 5, then the new mean and the mean deviation about the new mean, respectively, are

 

Option: 1

\bar{X},M.D.


Option: 2

\bar{X}+5,M.D.


Option: 3

\bar{X},M.D.+5


Option: 4

\bar{X}+5,M.D.+5


Answers (1)

best_answer

Observation all increased by 5

New\,\,mean=\frac{new\,\, sum}{n} = \frac{(x_1+5)+(x_2+5)+......+(x_n+5)}{n}

= \frac{x_1+x_2+......+x_n}{n} + \frac{5n}{n}

= \bar{X} + 5

 

New mean deviation about the new mean:

\\=\frac{1}{n}{\sum_{i=1}^{n}\left|(x_{i}+5)-(\bar X + 5)\right|}\\ = \frac{1}{n}{\sum_{i=1}^{n}\left|x_{i}-\bar X\right|}\\\\ = old \,\,mean\,\,deviation

So, \left ( \bar{X} \right )  mean will be increased by 5 but there will be no change in M.D

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Rishi

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