Mathematics 2009 JAMB Past Questions - Question 46: What is the mean deviation of x,2x,x+1 and 3x, if their mean is 2?

Correct Answer

D

Explanation

x-2+2x-2+(x+1)-2+3x-2=0x-2+2x-2-2x-2+3x-2=04x -8To find the mean deviation of a set of numbers, we need to calculate the average of the absolute differences between each number and the mean.Given that the mean of the numbers x, 2x, x+1, and 3x is 2, we can set up the equation:(x + 2x + (x+1) + 3x) / 4 = 2Simplifying the equation:7x + 1 = 87x = 7x = 1Now, we substitute the value of x back into the original set of numbers:x = 12x = 2x+1 = 23x = 3The set of numbers is {1, 2, 2, 3}.To calculate the mean deviation, we find the absolute difference between each number and the mean (2), sum them up, and divide by the number of elements (4):Mean deviation = (|1-2| + |2-2| + |2-2| + |3-2|) / 4              = (1 + 0 + 0 + 1) / 4              = 2 / 4              = 0.5Therefore, the mean deviation of the numbers x, 2x, x+1, and 3x, given that their mean is 2, is 0.5.4x = 8x=8/4 = 2