Times Spent in Rush-Hour Traffic A sample of 9 drivers shows the time that they spent (in minutes) stopped in rushhour traffic on a specific snowy day last winter. Round your answers to one decimal place. \[ \begin{array}{lllllllll} 52 & 71 & 63 & 58 & 70 & 47 & 65 & 54 & 56 \end{array} \] Send data to Excel Part 1 of 3 Find the range. The range is \( \square \) 24.0 Alternate Answer: The range is 24 . Part: \( 1 / 3 \) Part 2 of 3 Find the variance. The variance is \( \square \) .

To find the **variance** of the time spent by the 9 drivers in rush-hour traffic, follow these steps: ### Step 1: Calculate the Mean First, determine the average (mean) time. \[ \text{Mean} = \frac{52 + 71 + 63 + 58 + 70 + 47 + 65 + 54 + 56}{9} = \frac{536}{9} \approx 59.6 \text{ minutes} \] ### Step 2: Calculate Each Deviation from the Mean and Square It Next, subtract the mean from each data point and square the result: \[ \begin{align*} (52 - 59.6)^2 &\approx (-7.6)^2 = 57.8 \\ (71 - 59.6)^2 &\approx (11.4)^2 = 129.96 \\ (63 - 59.6)^2 &\approx (3.4)^2 = 11.56 \\ (58 - 59.6)^2 &\approx (-1.6)^2 = 2.56 \\ (70 - 59.6)^2 &\approx (10.4)^2 = 108.16 \\ (47 - 59.6)^2 &\approx (-12.6)^2 = 158.76 \\ (65 - 59.6)^2 &\approx (5.4)^2 = 29.16 \\ (54 - 59.6)^2 &\approx (-5.6)^2 = 31.36 \\ (56 - 59.6)^2 &\approx (-3.6)^2 = 12.96 \\ \end{align*} \] ### Step 3: Sum the Squared Deviations \[ 57.8 + 129.96 + 11.56 + 2.56 + 108.16 + 158.76 + 29.16 + 31.36 + 12.96 = 542.48 \] ### Step 4: Calculate the Variance Since this is a sample of drivers, we'll use the **sample variance** formula: \[ \text{Variance} = \frac{\sum (\text{deviations}^2)}{n - 1} = \frac{542.48}{9 - 1} = \frac{542.48}{8} \approx 67.8 \] ### **Final Answer:** The variance is **67.8**.