For the scores 1, 0, 2, 4, what is the value of Σ(X + 2)?

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Multiple Choice

For the scores 1, 0, 2, 4, what is the value of Σ(X + 2)?

Explanation:
The idea being tested is how sums behave when you add a constant to every observation. You can use linearity of summation: Σ(X+2) = ΣX + Σ2 = ΣX + 2n, where n is the number of observations. Here, n = 4 and the X-values sum to 1 + 0 + 2 + 4 = 7. So Σ(X+2) = 7 + 2×4 = 7 + 8 = 15. You can also check by adding the constants to each term: (1+2) + (0+2) + (2+2) + (4+2) = 3 + 2 + 4 + 6 = 15. So the value is 15.

The idea being tested is how sums behave when you add a constant to every observation. You can use linearity of summation: Σ(X+2) = ΣX + Σ2 = ΣX + 2n, where n is the number of observations.

Here, n = 4 and the X-values sum to 1 + 0 + 2 + 4 = 7. So Σ(X+2) = 7 + 2×4 = 7 + 8 = 15.

You can also check by adding the constants to each term: (1+2) + (0+2) + (2+2) + (4+2) = 3 + 2 + 4 + 6 = 15.

So the value is 15.

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