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The mean and mode of a set of data are 58.7 and 61.1, respectively. Find the median of the data, using the empirical formula.
59.5
55.2
54.6
55.8
59.5
Use the empirical relationship: Mode=3(Median)тИТ2(Mean). Plug in given values and solve for Median: 61.1=3(Median)тИТ2(58.7).
Mean = 58.7, Mode = 61.1
Mode=3├ЧMedianтИТ2├ЧMean
Use the empirical relationship: Mode=3(Median)тИТ2(Mean). Plug in given values and solve for Median: 61.1=3(Median)тИТ2(58.7).
Confusing the coefficient order: remember that Mean has a weight of 2 and Median has a weight of 3 (3├ЧMedianтИТ2├ЧMean).
Identify empirical formula
The relationship between Mean, Median, and Mode for a moderately skewed distribution is given by the empirical formula.
Mode=3├ЧMedianтИТ2├ЧMean
Substitute given values
Substitute the values of Mode (61.1) and Mean (58.7) into the formula.
61.1=3├ЧMedianтИТ2├Ч58.7
Solve for Median
First, calculate 2├Ч58.7=117.4. Then, add 117.4 to both sides: 61.1+117.4=3├ЧMedian. This gives 178.5=3├ЧMedian. Finally, divide by 3.
Median=3178.5тАЛ=59.5
A is correct because the calculation Median=(61.1+117.4)/3 results in 59.5.
This formula is frequently tested in statistics problems across RRB and SSC exams to relate the three measures of central tendency.
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