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# The empirical relationship between mean, median and mode is:A.${\text{Mean}} > {\text{Median}} > {\text{Mode}}$B.${\text{Mean}} = {\text{Median}} = {\text{Mode}}$C.${\text{Mode}} - {\text{Mean}} = 3\left( {{\text{Median}} - {\text{Mean}}} \right)$D.${\text{Mean}} - {\text{Mode}} = 3\left( {{\text{Mean}} - {\text{Median}}} \right)$

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Hint: First we will use the formula of the relationship between mean, median and mode is ${\text{Mode}} = 3{\text{Median}} - 2{\text{Mean}}$. Then simplify the given relationship by adding and subtracting Mean on both sides to find the required value.

Complete step-by-step answer:
We know that the formula of the relationship between mean, median and mode is ${\text{Mode}} = 3{\text{Median}} - 2{\text{Mean}}$.

Subtracting and adding the value of mean in the above formula of relationship to find the empirical relationship, we get
$\Rightarrow {\text{Mode}} - {\text{Mean}} = 3{\text{Median}} - 2{\text{Mean}} - {\text{Mean}} \\ \Rightarrow {\text{Mode}} - {\text{Mean}} = 3{\text{Median}} - 3{\text{Mean}} \\$
Taking the 3 common from the right hand side of the above equation, we get
$\Rightarrow {\text{Mode}} - {\text{Mean}} = 3\left( {{\text{Median}} - {\text{Mean}}} \right)$
Therefore, the required value is ${\text{Mode}} - {\text{Mean}} = 3\left( {{\text{Median}} - {\text{Mean}}} \right)$.

Hence, option C is correct.

Note: We know that the mean or an average of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set. The median is the middle value when a data set is ordered from least to greatest. The mode is the number that occurs most often in a data set.
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