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 $$ \square $$ .

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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**.
The variance is 67.8.

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