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If the mean of a distribution is 8.73 and its median is 11, then the mode of the distribution is __________ (using empirical relation).
15.54
19.73
22
17.46
15.54
Use the empirical relationship between mean, median, and mode: Mode = 3(Median) - 2(Mean). Directly substitute the given values.
Mean = 8.73, Median = 11
Mode=3├ЧMedianтИТ2├ЧMean
Use the empirical relationship between mean, median, and mode: Mode = 3(Median) - 2(Mean). Directly substitute the given values.
Confusing the coefficients of Median and Mean in the empirical formula (it is 3 times Median minus 2 times Mean).
State the Empirical Formula
For a moderately asymmetrical distribution, the empirical relationship connecting mean, median, and mode is given by: Mode=3├ЧMedianтИТ2├ЧMean
Mode=3├ЧMedianтИТ2├ЧMean
Substitute the Given Values
Substitute Mean=8.73 and Median=11 into the formula: Mode=3(11)тИТ2(8.73)
Mode=3(11)тИТ2(8.73)
Calculate the Result
Multiply the values: 3├Ч11=33 and 2├Ч8.73=17.46. Subtract them: Mode=33тИТ17.46=15.54
Mode=15.54
A is correct because the calculated mode using the empirical relation is 15.54.
In statistics questions involving skewed distributions, always check whether you need to use the empirical formula connecting mean, median, and mode (Mode = 3 Median - 2 Mean).
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