For the monthly incomes of a colony the mean is ₹18,600 and the mode is ₹17,400. Estimate the median income using the empirical relation.

The empirical relation Mode = 3 Median − 2 Mean rearranges to $3\text{Median}=\text{Mode}+2\text{Mean}$. So $3\text{Median}=17400+2\times 18600=54600$ and Median = ₹18,200. ₹18,000 is simply the average of the mean and the mode, which the relation does NOT say. ₹17,800 swaps the roles of mean and mode, computing $\frac{2\times 17400+18600}{3}$. ₹21,000 uses the relation backwards as $3\text{Mean}-2\text{Mode}$.