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 − Mean = 12

We know that

Mode = 3Median − 2Mean

∴ Mode − Mean = 3(Median − Mean)

⇒ 12 = 3(Median − Mean)

⇒ Median − Mean = 4 .....(1)

Again,

Mode = 3Median − 2Mean

⇒ 2Mode = 6Median − 4Mean

⇒ Mode − Mean + Mode = 6Median − 5Mean

⇒ 12 + (Mode − Median) = 5(Median − Mean)

⇒12 + (Mode − Median) = 20 [Using (1)]

⇒ Mode − Median = 20 − 12 = 8

Hence, the correct option is (b).