What is the mean deviation of x, 2x, x+1 and 3x. If their mean is 2?
A
0.5
B
1.0
C
1.5
D
2.0
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
x
∴x
x-\(\overline{X}\)
/x-\(\overline{X}\)/
x
1
-1
1
2x
2
0
0
x+1
2
0
0
3x
3
1
1
∑/x-\(\overline{X}\)/ = 2
Mean(\(\overline{X}\)) = \(\frac{ x + 2x + x + 1 + 3x}{4}\) = 2
2 = \(\frac{7x + 1}{4}\)
8 = 7x + 1
7x = 8 - 1 = 7
x = \(\frac{7}{7}\) = 1
Mean deviation = \(\frac{∑(| x - \overline{X}|)}{n}\)
M.D = \(\frac{2}{4}\) = \(\frac{1}{2}\) = 0.5
Source: Myschool Past Questions Archive (Record #9407)