The mean and the median of a dataset are in the ratio 9:8. Using the empirical formula for moderately skewed distributions, determine the ratio of the median to the mode.
4 : 3
For a moderately skewed distribution, the empirical relation is: Mode = 3 × Median − 2 × Mean.
Let Mean = 9k and Median = 8k, where k is a positive constant.
Mode = 3(8k) − 2(9k) = 24k − 18k = 6k.
Ratio of Median to Mode = 8k : 6k = 4 : 3.
Hence, the correct answer is 4 : 3.
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