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

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Multiple Choice

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

Explanation:
The concept here is summing squared deviations from a fixed value. You take each score, subtract the fixed value (2), square the result, and add them up. For scores 2, 3, 5: - 2 - 2 = 0, squared is 0 - 3 - 2 = 1, squared is 1 - 5 - 2 = 3, squared is 9 Add them: 0 + 1 + 9 = 10. So the value is 10. This differs from the variance, which uses deviations from the mean rather than from a fixed value. If you computed deviations from the mean instead, you’d get about 4.667.

The concept here is summing squared deviations from a fixed value. You take each score, subtract the fixed value (2), square the result, and add them up.

For scores 2, 3, 5:

  • 2 - 2 = 0, squared is 0

  • 3 - 2 = 1, squared is 1

  • 5 - 2 = 3, squared is 9

Add them: 0 + 1 + 9 = 10.

So the value is 10. This differs from the variance, which uses deviations from the mean rather than from a fixed value. If you computed deviations from the mean instead, you’d get about 4.667.

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