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  4. If the difference between the mean and median of a data is 2 x, then find the difference between the mean and mode of the data?

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Q. If the difference between the mean and median of a data is $2 x$, then find the difference between the mean and mode of the data?

Statistics

Solution:

$\text { Mode }=3 \text { median }-2 \text { mean }$
$ \text { Mode }- \text { mean }=3 \text { median }-3 \text { mean } $
$ \text { Mode }- \text { Mean }=3(\text { Median }- \text { mean }) $
$\therefore \text { Mode }- \text { mean }=3(2 x)=6 x $
$ (\text { Since, } \text { median }- \text { mean }=x)$