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Using the empirical relation between the mean, median and mode, find the value of the mode if the median is 30 and mean is 25.
40
60
50
30
40
Remember the mnemonic 3-2-1 for Mode, Median, Mean: Mode = 3(Median) - 2(Mean).
Median = 30, Mean = 25
Mode=3├ЧMedianтИТ2├ЧMean
Remember the mnemonic 3-2-1 for Mode, Median, Mean: Mode = 3(Median) - 2(Mean).
Students often swap the coefficients and calculate 2├ЧMedianтИТ3├ЧMean or add them instead of subtracting.
Identify the Empirical Relationship
The relationship between the three measures of central tendency for moderately skewed distributions is given by the formula:
Mode=3(Median)тИТ2(Mean)
Substitute the Given Values
Substitute the provided values for the median and the mean into the formula:
Mode=3(30)тИТ2(25)
Perform Calculation
Calculate the products first and then find the difference:
Mode=90тИТ50=40
A is correct because substituting the values into the formula Mode=3(30)тИТ2(25) gives 90тИТ50=40.
This relation is frequently tested in exams; remember that Mean, Median, and Mode are linked by this simple linear equation, which can also be rearranged to find one if the other two are known.
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