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For a frequency distribution, the mean is 25 and the median is 22. Using the empirical formula, what is the mode of the data?
16
18
20
28
16
Memorize the sequence: 3 Median - 2 Mean = Mode. Remember that the mode is pulled closer to the mean than the median in a skewed distribution, so the result (16) is logically lower than the median (22).
Mean = 25, Median = 22
Mode=3(Median)тИТ2(Mean)
Memorize the sequence: 3 Median - 2 Mean = Mode. Remember that the mode is pulled closer to the mean than the median in a skewed distribution, so the result (16) is logically lower than the median (22).
Many students accidentally calculate 2├ЧMedianтИТ3├ЧMean or misplace the coefficients, which leads to incorrect results.
State the empirical formula
The Pearson's empirical relation for a moderately skewed frequency distribution is given by the formula:
Mode=3├ЧMedianтИТ2├ЧMean
Substitute the given values
Given that Mean=25 and Median=22, substitute these into the equation:
Mode=3(22)тИТ2(25)
Perform the calculation
Calculate the products and find the difference:
Mode=66тИТ50=16
A is correct because substituting the given values into the empirical formula Mode=3(Median)тИТ2(Mean) results in 66тИТ50=16.
This formula is frequently tested in exams; remember the mnemonic 'Mode = 3 Median minus 2 Mean'. It is often used in Data Interpretation and Statistics modules of competitive aptitude tests.