WAEC 2012 Mathematics · Question 36

Given that the mean of the scores 15, 21, 17, 26, 18 and 29 is 21, calculate the standard deviation of the scores

Options

A. $\sqrt{10}$
B.4
C.5
D. $\sqrt{30}$

Answer: C. 5

Explanation written with AI and checked against the answer key

The question says the mean is 21, so let's check the data first. Sum = 15 + 21 + 17 + 26 + 18 + 29 = 126, and 126 ÷ 6 = 21. ✓ Step 1: Find the deviations from the mean (x − 21) | x | x − 21 | (x − 21)² | |---|---|---| | 15 | −6 | 36 | | 21 | 0 | 0 | | 17 | −4 | 16 | | 26 | 5 | 25 | | 18 | −3 | 9 | | 29 | 8 | 64 | Step 2: Sum of squared deviations 36 + 0 + 16 + 25 + 9 + 64 = 150 Step 3: Standard deviation The formula used in WASSCE is σ = √(Σ(x − x̄)² / n): σ = √(150 / 6) = √25 = 5 Answer: C (5) Tip: In WASSCE, standard deviation questions at this level divide by n (not n − 1). Always find the mean, then deviations, square them, sum, divide by n, and take the square root. Check that the sum of the deviations is zero (−6 + 0 − 4 + 5 − 3 + 8 = 0 ✓) to catch arithmetic slips early.

AI can make mistakes. Report anything that looks wrong.