JAMB - Mathematics (2009 - No. 42)
What is the mean deviation of x, 2x, x+1 and 3x. If their mean is 2?
0.5
1.0
1.5
2.0
Explanation
| 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
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