What is the value of Σ(X - 2) for the scores 2, 3, 5?

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Multiple Choice

What is the value of Σ(X - 2) for the scores 2, 3, 5?

Explanation:
The question hinges on summing deviations from a fixed value. You take each score and subtract the chosen constant, then add those results together. Subtracting 2 from each score gives 0, 1, and 3. Adding them up yields 0 + 1 + 3 = 4, so the value is 4. In general, this sum equals the total of the scores minus the number of scores times the constant (ΣX − n·a). The mean of the data here is (2 + 3 + 5) / 3 = 10/3, and if you summed deviations from the mean, they would cancel to zero. The anchor you choose matters—the sum of deviations from 2 is 4, not zero.

The question hinges on summing deviations from a fixed value. You take each score and subtract the chosen constant, then add those results together. Subtracting 2 from each score gives 0, 1, and 3. Adding them up yields 0 + 1 + 3 = 4, so the value is 4. In general, this sum equals the total of the scores minus the number of scores times the constant (ΣX − n·a). The mean of the data here is (2 + 3 + 5) / 3 = 10/3, and if you summed deviations from the mean, they would cancel to zero. The anchor you choose matters—the sum of deviations from 2 is 4, not zero.

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