 # 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.${\text{Mean}} - {\text{Mode}} = 3\left( {{\text{Mean}} - {\text{Median}}} \right)$ Verified
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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.

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.  Download Practice Questions