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If the mean and the mode of a particular data set are 36 and 63, respectively, then, using an empirical relation, find the value of the median of the same data set.
55
45
40
39
45
Use the relationship Median=3Mode+2├ЧMeanтАЛ. With given values: (63+72)/3=135/3=45.
Mean = 36, Mode = 63
Mode=3├ЧMedianтИТ2├ЧMean
Use the relationship Median=3Mode+2├ЧMeanтАЛ. With given values: (63+72)/3=135/3=45.
Students often misremember the empirical relation as Mode=3├ЧMeanтИТ2├ЧMedian or Mode=2├ЧMedianтИТ3├ЧMean, which leads to incorrect answers.
State the empirical formula
The empirical relationship between Mean, Median, and Mode for a moderately skewed distribution is given by the formula:
Mode=3├ЧMedianтИТ2├ЧMean
Substitute the known values
Substitute Mean=36 and Mode=63 into the equation:
63=3├ЧMedianтИТ2├Ч36
Simplify and solve for Median
First calculate 2├Ч36=72, then add it to both sides: 63+72=3├ЧMedian, which simplifies to 135=3├ЧMedian. Dividing by 3 gives the median:
Median=3135тАЛ=45
B is correct because calculating the median using the empirical relation Mode=3├ЧMedianтИТ2├ЧMean yields Median=45.
This empirical relation is a classic frequent topic in RRB exams. Remember the '3-2-1' rule: Mode=3(Median)тИТ2(Mean).
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