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The mean of a data set is 25 and its median is 35. The mode (using empirical relation) of the data is:
45
50
55
60
55
Remember the mnemonic 'Mode is 3 times Median minus 2 times Mean' (3тИТ2=1), which ensures you subtract the correct multiplier.
Mean = 25, Median = 35
Mode=3├ЧMedianтИТ2├ЧMean
Remember the mnemonic 'Mode is 3 times Median minus 2 times Mean' (3тИТ2=1), which ensures you subtract the correct multiplier.
Students often swap the coefficients and calculate 2├ЧMedianтИТ3├ЧMean which leads to an incorrect result.
State the empirical relationship
The relationship between mean, median, and mode for a moderately skewed distribution is given by the Pearson's empirical formula.
Mode=3├ЧMedianтИТ2├ЧMean
Substitute given values
Plug the given mean (25) and median (35) values into the formula.
Mode=3(35)тИТ2(25)
Calculate the result
Perform the arithmetic multiplication and subtraction: 3├Ч35=105 and 2├Ч25=50.
Mode=105тИТ50=55
C is correct because applying the formula Mode=3(35)тИТ2(25) results in 55.
This empirical relationship is frequently tested in exams alongside the concept of 'Skewness', where MeanтИТMode=3(MeanтИТMedian).