A magazine reports that for the daily earnings of street vendors the mean is ₹420 and the median is ₹450, and it prints the mode as ₹480. Judged by the empirical relation, the printed mode is:

Mode = 3 Median − 2 Mean = $3\times 450-2\times 420=1350-840=510$. The printed ₹480 falls $510-480=30$ short of this. 'Too high by ₹120' comes from applying the relation the wrong way round as $3\text{Mean}-2\text{Median}=1260-900=360$. The relation is an approximation, but it is exactly what makes a quick consistency check possible — the raw data is not needed. Note the ordering it predicts: Mean (420) < Median (450) < Mode (510), the signature of a left-skewed set.