Which expression represents subtracting four from each value, squaring the result, and summing across all values?

Which expression represents subtracting four from each value, squaring the result, and summing across all values?

• A. Sum of X minus four, squared
• B. Sum of X squared minus four
• C. Sum of (X minus four) squared
• D. Sum of X minus four

Answer: (C)

Subtracting four from each value, squaring the result, and then summing across all values is exactly computing the sum of squared deviations from four. For each data point X_i, you take X_i minus 4, square that difference, and add those squared differences over all observations. This is written as the sum of (X_i - 4)^2, which is why the correct expression is the sum of (X minus four) squared. The other forms don’t match this sequence: squaring after summing would be (Σ X_i - 4)^2, which isn’t the same as summing the squared differences; squaring the X values first and then subtracting four isn’t about deviations from four; and summing without squaring misses the emphasis on squared deviations.

Subtracting four from each value, squaring the result, and then summing across all values is exactly computing the sum of squared deviations from four. For each data point X_i, you take X_i minus 4, square that difference, and add those squared differences over all observations. This is written as the sum of (X_i - 4)^2, which is why the correct expression is the sum of (X minus four) squared.

The other forms don’t match this sequence: squaring after summing would be (Σ X_i - 4)^2, which isn’t the same as summing the squared differences; squaring the X values first and then subtracting four isn’t about deviations from four; and summing without squaring misses the emphasis on squared deviations.