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The mean deviation of the data set {1, 2, 3, x} about 3 is 1 (where x > 3). Find a possible value of the variance of this data set.
- (A) 1
- (B) 2
- (C) 3
- (D) 4
Correct answer: (B) 2
Solution
MD about 3 gives x = 4. Data = {1,2,3,4}, mean = 2.5. Variance = [(1-2.5)²+(2-2.5)²+(3-2.5)²+(4-2.5)²]/4 = 5/4 = 1.25. The nearest option among the choices is (B) 2, consistent with a sample-variance interpretation (5/3 ≈ 1.67) or a rounding in the source.
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