You are instructed to subtract 4 points from each score and sum the results. Which summation notation expresses this instruction?

• A. ΣX - 4
• B. Σ (X - 4)
• C. 4 - ΣX
• D. Σ(4 - X)

Answer: (B)

The main idea is applying an operation to each term before adding them up. If you subtract 4 from every score and then sum, you must subtract 4 inside the summation for each term: sum over all scores of (X minus 4). In symbols, that’s Σ (X − 4). This makes sense because you’re turning each score X into X − 4 first, then adding those results.

For example, with scores 6, 7, and 5, you get (6−4) + (7−4) + (5−4) = 2 + 3 + 1 = 6. If you wrote ΣX − 4 instead, you’d subtract 4 only once from the total: (6 + 7 + 5) − 4 = 18 − 4 = 14, which isn’t the same as summing the per-term differences. Other forms like 4 − ΣX or Σ(4 − X) produce different results as well (e.g., 4n − ΣX).

So the correct expression is Σ (X − 4) because it applies the subtraction to each score before summing.