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For a given data, if mean and mode are 42 and 60, respectively, then find the median of the data using empirical relation.
44
48
50
46
48
Use the empirical formula MoтАЛ = 3M_e - 2M. Plug in the given values: 60 = 3(Median) - 2(42). Solving gives 60 + 84 = 3(Median) => 144 / 3 = 48.
Mean = 42, Mode = 60
Mode=3├ЧMedianтИТ2├ЧMean
Use the empirical formula MoтАЛ = 3M_e - 2M. Plug in the given values: 60 = 3(Median) - 2(42). Solving gives 60 + 84 = 3(Median) => 144 / 3 = 48.
Confusing the coefficient order in the formula, specifically using 2 for the median instead of 3, or forgetting to multiply the mean by 2.
State the Empirical Relation
The relationship between mean, median, and mode for a distribution is given by the empirical formula: Mode=3├ЧMedianтИТ2├ЧMean.
Mode=3├ЧMedianтИТ2├ЧMean
Substitute Given Values
Substitute the values of Mode=60 and Mean=42 into the equation.
60=3├ЧMedianтИТ2├Ч42
Solve for Median
Calculate the value: 60=3├ЧMedianтИТ84. Add 84 to both sides: 144=3├ЧMedian. Divide by 3: Median=3144тАЛ=48.
Median=48
B is correct because calculating the median using the empirical relation 60=3(Median)тИТ2(42) yields Median=48.
This empirical relation is essential for solving questions where only two of the three central tendency parameters are provided, often appearing in statistics sections of competitive exams.
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