Question 27:
In a moderately skewed data distribution, the ratio of the arithmetic mean to the median is 4 : 5. If the sum of the mean and the median is 90, what is the mode of this distribution?
Options :
- a) 65
- b) 70
- c) 60
- d) 75
correct answer : b)
Explanation :
Let Mean = 4x and Median = 5x.
Given 4x + 5x = 90 ⇒ 9x = 90 ⇒ x = 10.
So, Mean = 40 and Median = 50.
Using empirical formula: Mode = 3(Median) – 2(Mean) = 3(50) – 2(40) = 150 – 80 = 70.