Question

If mode of a series exceeds its mean by 12, then mode exceeds the median by 

A. 4 

B. 8 

C. 6 

D. 10

Answer 1

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.