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The mean of a data set is 55 and its median is 61. Calculate the mode using the empirical relation: Mode = 3(Median) - 2(Mean).
73
71
67
69
73
Use the unit digit trick: 3├Ч1=3 and 2├Ч5=10. The calculation becomes 3тИТ0=3 at the units place. Option A (73) ends in 3, making it the most probable answer.
Mean = 55, Median = 61
Mode=3(Median)тИТ2(Mean)
Use the unit digit trick: 3├Ч1=3 and 2├Ч5=10. The calculation becomes 3тИТ0=3 at the units place. Option A (73) ends in 3, making it the most probable answer.
Students often swap the coefficients 2 and 3, using 2├ЧMedianтИТ3├ЧMean, which leads to an incorrect result.
Identify given values
Extract the Mean and Median from the problem statement.
Mean=55,Median=61
Substitute into the empirical formula
Apply the given empirical relationship to find the Mode.
Mode=3(61)тИТ2(55)
Perform the final calculation
Calculate the products and then the difference: 3├Ч61=183 and 2├Ч55=110. Subtract 183тИТ110=73.
Mode=183тИТ110=73
A is correct because the application of the empirical formula 3(61)тИТ2(55) yields exactly 73.
This empirical relation is specific to moderately skewed distributions; always verify if the data is symmetrical or skewed when choosing between Mean, Median, and Mode.