NECO 2005 Mathematics · Question 10

Find the standard deviation of the numbers 6, 9, 10, 8 and 7

Options

A.1.4
B.2
C.2.4
D.5
E.8

Answer: A. 1.4

Explanation written with AI and checked against the answer key

Analyze the question: We need the standard deviation of 6, 9, 10, 8, 7. Concept: Standard deviation is σ = √[Σ(x − x̄)² / n]. It measures how spread out the numbers are around the mean. Step 1: Find the mean x̄ = (6 + 9 + 10 + 8 + 7) / 5 = 40 / 5 = 8 Step 2: Find the deviations and square them | x | x − x̄ | (x − x̄)² | |---|-------|-----------| | 6 | −2 | 4 | | 9 | 1 | 1 | | 10 | 2 | 4 | | 8 | 0 | 0 | | 7 | −1 | 1 | Σ(x − x̄)² = 10 Step 3: Divide by n and take the square root σ = √(10/5) = √2 ≈ 1.414 ≈ 1.4 (If you used the sample formula, dividing by n − 1 = 4, you would get √2.5 ≈ 1.58, which is not an option. So the NECO/WASSCE population formula is the one intended.) Answer: A. 1.4. Tip: In Nigerian exams, use the formula dividing by n (not n − 1) unless told otherwise. Quick check: the numbers are all within 2 of the mean, so the standard deviation must be small, which rules out 5 and 8 immediately.

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