<p>The standard deviation of some temperature data in °C is 5. If the data were converted into °F, the new variance would be</p>
Step-by-Step Solution
Key Concept: Variance scales with the square of the linear transformation coefficient. When converting °C to °F using F = (9/5)C + 32, only the scaling factor (9/5) affects variance; the additive constant (32) doesn't affect spread.
<p><strong>Step 1:</strong> Recall that for a linear transformation Y = aX + b, the variance transforms as Var(Y) = a²·Var(X). The additive constant b doesn't affect variance.</p><p><strong>Step 2:</strong> The conversion formula is °F = (9/5)°C + 32. Here, a = 9/5 and b = 32.</p><p><strong>Step 3:</strong> Given: SD in °C = 5, so Variance in °C = 5² = 25</p><p><strong>Step 4:</strong> New Variance in °F = (9/5)² × 25 = (81/25) × 25 = 81</p><p><strong>Step 5:</strong> Alternatively: New SD in °F = (9/5) × 5 = 9, so New Variance = 9² = 81</p><p>∴ Answer: <strong>81</strong></p>
Correct Answer: A