If mode of a series exceeds its mean by 12, then mode exceeds the median by
Given, mode exceeds mean by 12 i.e. mode - mean = 12 …[1]
We know that empirical relation between mean, median and mode is
Mode = 3 Median - 2 Mean
⇒ 3 Mode - 2 Mode = 3 Median - 2 Mean
⇒ 3 Mode - 3 Median = 2 Mode - 2 Mean
⇒ 3(Mode - Median) = 2(Mode - Mean)
From [1] we have
3(Mode - Median) = 2(12)
⇒ Mode - Median = 8
i.e. Mode exceeds Median by 8.