<p>What is the standard deviation of the following data?</p><table border='1'><tr><th>Measurement</th><td>0–10</td><td>10–20</td><td>20–30</td><td>30–40</td></tr><tr><th>Frequency</th><td>1</td><td>3</td><td>4</td><td>2</td></tr></table>
Step-by-Step Solution
Key Concept: Standard deviation requires finding the mean first using class midpoints, then calculating the sum of squared deviations weighted by frequencies. The formula σ = √[Σf(x-x̄)²/Σf] must be applied carefully with grouped data.
<p><strong>Step 1:</strong> Find class midpoints and total frequency.</p><p>Midpoints: 5, 15, 25, 35</p><p>Frequencies: 1, 3, 4, 2</p><p>Total frequency (N) = 1 + 3 + 4 + 2 = 10</p><p><strong>Step 2:</strong> Calculate mean x̄.</p><p>x̄ = [1(5) + 3(15) + 4(25) + 2(35)]/10 = (5 + 45 + 100 + 70)/10 = 220/10 = 22</p><p><strong>Step 3:</strong> Calculate Σf(x - x̄)².</p><p>f₁(x₁ - x̄)² = 1(5-22)² = 1(289) = 289</p><p>f₂(x₂ - x̄)² = 3(15-22)² = 3(49) = 147</p><p>f₃(x₃ - x̄)² = 4(25-22)² = 4(9) = 36</p><p>f₄(x₄ - x̄)² = 2(35-22)² = 2(169) = 338</p><p>Σf(x - x̄)² = 289 + 147 + 36 + 338 = 810</p><p><strong>Step 4:</strong> Calculate standard deviation.</p><p>σ = √(810/10) = √81 = <strong>9</strong></p><p>∴ Answer: C</p>
Correct Answer: C