Discussion
The empirical formula used to know mode is ................. .
Answer: C
The empirical formula is Mode = 3 Median - 2 Mean.
Karl Pearson observed that in a moderately skewed distribution the median lies about one-third of the way from the mean to the mode, which gives:
\[ \begin{aligned} \text{Mean} - \text{Mode} &= 3(\text{Mean} - \text{Median}) \\ \text{Mode} &= 3\,\text{Median} - 2\,\text{Mean} \end{aligned} \]
It is used when the mode is ill-defined. The option '2 Mean - 3 Median' is the same expression with the wrong sign, and the versions with 'Mean - 2 Median' or a plus sign do not follow from the relation at all.
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