Measures of Central Tendency — Economics STD 11 Commerce — Question
CBSE BoardEnglish MediumSTD 11 CommerceEconomicsMeasures of Central Tendency1 Mark
Question
Taking some hypothetical data, show that sum of deviations taken from mean is zero.
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Answer
The sum of the deviations, of all the values of x, from their arithmetic mean, is zero.Justification:
$\sum\text{f}_\text{i}(\text{x}_\text{i}-\overline{\text{x}})=\sum\text{f}_\text{i}\text{x}_\text{i}-\overline{\text{x}}\sum\text{f}_\text{i}=0$
$\overline{\text{x}}=\frac{\sum{\text{f}_\text{i}}\text{x}_\text{i}}{\sum\text{f}_\text{i}}$
$\therefore\ \sum\text{f}_\text{i}\text{x}_\text{i}=\overline{\text{x}}\sum\text{f}_\text{i}$
Since $\overline{\text{x}}$ is a constant.
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