Traveler Spending The data show the traveler spending in billions of dollars for a recent year for a sample of the states. Round your answers to two decimal places. $$ \begin{array}{llllllllllll} 20.9 & 33.1 & 21.8 & 58.5 & 23.5 & 110.9 & 30.4 & 24.9 & 74.1 & 60.3 & 40.4 & 45.4 \end{array} $$ Send data to Excel Part 1 of 3 Find the range. The range is 90.00 . Part: $$ 1 / 3 $$ Part 2 of 3 Find the variance. The variance is $$ \square $$ .

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To calculate the **variance** of the traveler spending data, follow these steps:

### **1. Data Set:**
$$
20.9,\ 33.1,\ 21.8,\ 58.5,\ 23.5,\ 110.9,\ 30.4,\ 24.9,\ 74.1,\ 60.3,\ 40.4,\ 45.4
$$

### **2. Calculate the Mean ($$\bar{x}$$):**
$$
\bar{x} = \frac{\sum x_i}{n} = \frac{544.2}{12} = 45.35
$$

### **3. Compute Each Squared Deviation $$(x_i - \bar{x})^2$$:**

$$
\begin{array}{ll}
(20.9 - 45.35)^2 = 597.80 \
(33.1 - 45.35)^2 = 150.06 \
(21.8 - 45.35)^2 = 554.60 \
(58.5 - 45.35)^2 = 172.22 \
(23.5 - 45.35)^2 = 477.22 \
(110.9 - 45.35)^2 = 4292.80 \
(30.4 - 45.35)^2 = 223.00 \
(24.9 - 45.35)^2 = 418.03 \
(74.1 - 45.35)^2 = 826.56 \
(60.3 - 45.35)^2 = 223.00 \
(40.4 - 45.35)^2 = 24.50 \
(45.4 - 45.35)^2 = 0.00 \
\end{array}
$$

**Total Squared Deviations:**
$$
597.80 + 150.06 + 554.60 + 172.22 + 477.22 + 4292.80 + 223.00 + 418.03 + 826.56 + 223.00 + 24.50 + 0.00 = 7959.79
$$

### **4. Calculate the Variance ($$s^2$$):**
$$
s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1} = \frac{7959.79}{11} \approx 723.62
$$

### **Final Answer:**
The **variance** of the traveler spending data is **723.62** (in billions of dollars squared).
The variance of the traveler spending data is 723.62 (in billions of dollars squared).

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