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  4. If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is

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Q. If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is

JamiaJamia 2011

Solution:

Given, $ \sum\limits_{i=1}^{20}{({{x}_{i}}-30)=20} $ $ \Rightarrow $ $ \sum\limits_{i=1}^{20}{{{x}_{i}}-20\times 30=20} $ $ \Rightarrow $ $ \sum\limits_{i=1}^{20}{{{x}_{i}}}=620 $ $ \therefore $ Mean $ =\frac{\sum\limits_{i=1}^{20}{{{x}_{i}}}}{20}=\frac{620}{20}=31 $