Difference of mode and median, mode - median = 24 …[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(24) = 2(Mode - Mean)
⇒ Mode - Mean = 36 …[2]
on substracting [1] from [2]
Mode - Mean - (Mode - Median) = 36 - 24
Mode - Mean - Mode + Median = 8
Median - Mode = 8
Hence,
difference between median and mode is 8.