QUESTION 7 Suppose the following data show the prices of 4 cars with similar characteristics that sold at a recent auction (in thousands of dollars): \( 6.6,5.0,10.7,7.3 \). Calculate the standard deviation of the sample of selling prices. (please express your answer using decimal places)

To calculate the **sample standard deviation** of the selling prices \( \{6.6, 5.0, 10.7, 7.3\} \) (in thousands of dollars), follow these steps: ### 1. Calculate the Sample Mean \[ \text{Mean} (\bar{x}) = \frac{6.6 + 5.0 + 10.7 + 7.3}{4} = \frac{29.6}{4} = 7.4 \] ### 2. Calculate Each Deviation from the Mean and Square It \[ \begin{align*} (6.6 - 7.4)^2 &= (-0.8)^2 = 0.64 \\ (5.0 - 7.4)^2 &= (-2.4)^2 = 5.76 \\ (10.7 - 7.4)^2 &= (3.3)^2 = 10.89 \\ (7.3 - 7.4)^2 &= (-0.1)^2 = 0.01 \\ \end{align*} \] ### 3. Sum the Squared Deviations \[ \text{Sum of squared deviations} = 0.64 + 5.76 + 10.89 + 0.01 = 17.3 \] ### 4. Calculate the Sample Variance Since we're dealing with a sample, divide by \( n-1 \) (where \( n = 4 \)): \[ \text{Variance} = \frac{17.3}{3} \approx 5.7667 \] ### 5. Calculate the Sample Standard Deviation \[ \text{Standard Deviation} = \sqrt{5.7667} \approx 2.40 \] ### **Final Answer** The standard deviation of the sample of selling prices is **2.40** thousand dollars.