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 $$ \square $$ .

Question

UpStudy AI · Accepted Answer

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).

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.

Send data to Excel

Part 1 of 3

Find the range.

The range is 90.00 .

Part:

Part 2 of 3

Find the variance.

The variance is .

Upstudy AI Solution

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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. Send data to Excel Part 1 of 3 Find the range. The range is 90.00 . Part: Part 2 of 3 Find the variance. The variance is .