Score (x) 0 1 2 3 4 5 6 Freq (f) 5 7 3 7 11 6 7 Find the variance

Analyze the question: We have a frequency table and need the variance of the scores.

Concept: Variance = Σfx²/Σf − (Σfx/Σf)²

Step 1: Total frequency Σf = 5 + 7 + 3 + 7 + 11 + 6 + 7 = 46

Step 2: Σfx

• 0×5 = 0
• 1×7 = 7
• 2×3 = 6
• 3×7 = 21
• 4×11 = 44
• 5×6 = 30
• 6×7 = 42

Σfx = 0 + 7 + 6 + 21 + 44 + 30 + 42 = 150

Mean = 150/46 = 3.2609

Step 3: Σfx²

• 0×5 = 0
• 1×7 = 7
• 4×3 = 12
• 9×7 = 63
• 16×11 = 176
• 25×6 = 150
• 36×7 = 252

Σfx² = 0 + 7 + 12 + 63 + 176 + 150 + 252 = 660

Step 4: Variance Σfx²/Σf = 660/46 = 14.3478 Mean² = (3.2609)² = 10.6333

Variance = 14.3478 − 10.6333 = 3.7145 ≈ 3.71

This is closest to option D (3.72). The small difference is a rounding matter: if the mean is rounded to 3.26, then 3.26² = 10.63 and the variance is 14.35 − 10.63 = 3.72, which matches D exactly.

Answer: D (3.72)

Tip: In frequency-table variance questions, build a table with columns f, fx and fx². Then use Σfx²/Σf − mean². Rounding the mean to 2 decimal places early is what produces the JAMB option value here, so if your answer is off by 0.01, pick the nearest option.