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The mean of a data is 41 and its median is 98. The mode (using empirical relation) of the data is:
209
240
128
212
212
Use the mnemonic 'Mode is the middle of the 3-2 swing': multiply the larger value (median) by 3 and subtract double the smaller value (mean).
Mean = 41, Median = 98
Mode=3├ЧMedianтИТ2├ЧMean
Use the mnemonic 'Mode is the middle of the 3-2 swing': multiply the larger value (median) by 3 and subtract double the smaller value (mean).
Students often accidentally swap the coefficients or calculate the expression as 2(Median) - 3(Mean) instead of the correct 3(Median) - 2(Mean).
State the empirical relationship
The relationship between Mean, Median, and Mode for a moderately skewed distribution is defined by Pearson's empirical formula.
Mode=3(Median)тИТ2(Mean)
Substitute given values
Substitute the values of Mean = 41 and Median = 98 into the formula.
Mode=3(98)тИТ2(41)
Perform multiplication
Calculate the individual terms: 3├Ч98=294 and 2├Ч41=82.
Mode=294тИТ82
Final calculation
Subtract the products to find the Mode.
Mode=212
D is correct because the calculation 3(98)тИТ2(41) results in 294тИТ82=212.
This empirical formula is a specific case of the relationship in frequency distributions; it is frequently tested in both Statistics and Data Interpretation sections.
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