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
Solution:
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).
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.