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The mean of a data is 20 and its median is 30. The mode (using empirical relation) of the data is:
131
50
110
44
50
Remember the mnemonic 'Mode is the middle of the 3-2 sequence', where Mode = 3(Median) - 2(Mean). Simply calculate 3 times 30 minus 2 times 20: 90 - 40 = 50.
Mean = 20, Median = 30
Mode=3├ЧMedianтИТ2├ЧMean
Remember the mnemonic 'Mode is the middle of the 3-2 sequence', where Mode = 3(Median) - 2(Mean). Simply calculate 3 times 30 minus 2 times 20: 90 - 40 = 50.
Students often misremember the empirical formula as 2(Median) - 3(Mean) or mix up the coefficients, leading to incorrect values.
Identify given values
The mean is given as 20 and the median is given as 30.
Mean=20,Median=30
Apply Empirical Relation
Use the standard relationship between Mean, Median, and Mode: Mode=3(Median)тИТ2(Mean).
Mode=3(30)тИТ2(20)
Perform calculation
Substitute the values into the formula to find the mode: 90тИТ40=50.
Mode=50
B is correct because the empirical formula yields 3(30)тИТ2(20)=50.
This empirical relation (Karl Pearson's formula) is specific to moderately skewed distributions; always check if the distribution type is mentioned in more advanced probability questions.
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