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The empirical relationship between mean, median and mode is: A.Mean>Median>Mode B.Mean=Median=Mode C.Mode−Mean=3(Median−Mean) D.Mean−Mode=3(Mean−Median)

The empirical relationship between mean, median and mode is:
A.Mean>Median>Mode

B.Mean=Median=Mode

C.Mode−Mean=3(Median−Mean)

D.Mean−Mode=3(Mean−Median)

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
20 days ago
Hint: First we will use the formula of the relationship between mean, median and mode is Mode=3Median−2Mean . 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 Mode=3Median−2Mean . Subtracting and adding the value of mean in the above formula of relationship to find the empirical relationship, we get ⇒Mode−Mean=3Median−2Mean−Mean⇒Mode−Mean=3Median−3Mean Taking the 3 common from the right hand side of the above equation, we get ⇒Mode−Mean=3(Median−Mean) Therefore, the required value is Mode−Mean=3(Median−Mean) . 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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