WAEC 2020 Mathematics · Question 9

The mean of the numbers 15, 21, 17, 26, 18, and 29 is 21. Calculate the standard deviation

Options

Answer: C. 5

Explanation written with AI and checked against the answer key

Step 1: Analyze the question We need the standard deviation of 15, 21, 17, 26, 18, 29, with mean 21 (check: 15+21+17+26+18+29 = 126, and 126 ÷ 6 = 21 ✓). Step 2: Concept Standard deviation: σ = √[Σ(x − mean)² / n] Step 3: Solution | x | x − 21 | (x − 21)² | |---|--------|-----------| | 15 | −6 | 36 | | 21 | 0 | 0 | | 17 | −4 | 16 | | 26 | 5 | 25 | | 18 | −3 | 9 | | 29 | 8 | 64 | Σ(x − mean)² = 36 + 0 + 16 + 25 + 9 + 64 = 150 Variance = 150 ÷ 6 = 25 Standard deviation = √25 = 5 Step 4: Answer The standard deviation is 5, which is option C. Tip: In WASSCE, the standard deviation of ungrouped data uses division by n (not n − 1). Build a table of deviations, square them, add, divide by n, then take the square root. The numbers are often chosen so the variance is a perfect square, such as 25 here, so if you get a perfect square, you are probably on track.

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