WAEC 2019 Mathematics · Question 23

Calculate the variance of 2, 4, 7, 8 and 9

Options

A.7.2
B.6.8
C.3.5
D.2.6

Answer: B. 6.8

Explanation written with AI and checked against the answer key

Step 1: Analyze the question We need the variance of the data set 2, 4, 7, 8, 9 (n = 5). Step 2: Concept Variance = Σ(x − mean)² ÷ n (the population formula, which is what WASSCE normally uses for this kind of question). Step 3: Solution Mean = (2 + 4 + 7 + 8 + 9) ÷ 5 = 30 ÷ 5 = 6 | x | x − 6 | (x − 6)² | |---|-------|----------| | 2 | −4 | 16 | | 4 | −2 | 4 | | 7 | 1 | 1 | | 8 | 2 | 4 | | 9 | 3 | 9 | Σ(x − mean)² = 16 + 4 + 1 + 4 + 9 = 34 Variance = 34 ÷ 5 = 6.8 (If you divided by n − 1 = 4, you would get 8.5, which is not among the options, so the population formula is the one intended.) Step 4: Answer The variance is 6.8, which is option B. Tip: In WASSCE and JAMB, unless the question says "sample variance", divide by n. A quick check: variance = (Σx²/n) − mean². Here Σx² = 4 + 16 + 49 + 64 + 81 = 214, so 214/5 − 36 = 42.8 − 36 = 6.8 ✓.

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