Questions: Listed below in order are prices in dollars for a Big Mac hamburger in the United States, Canada, Mexico, China, Japan, Russia, Switzerland, Italy, Spain, Britain, India, and Egypt. Such data are used to compare currency exchange rates and the costs of goods in different countries. Find the range, variance, and standard deviation for the given sample data. What do the measures of variation tell us about the prices of a Big Mac in different countries? 5.30, 5.30, 2.56, 3.21, 3.38, 2.31, 6.80, 5.08, 4.80, 4.43, 2.81, 1.87 The variance is 2.28 dollars. The standard deviation is 1.51 dollars. What do the measures of variation tell us about the prices of a Big Mac in different countries? A. The variance and standard deviation tell us that Big Macs have lower prices in wealthier countries. B. The range alone tells us that there are very small differences among prices of Big Mac hamburgers in different countries. C. The variance and standard deviation tell us that Big Macs have higher prices in wealthier countries. D. The range alone tells us that there are very substantial differences among prices of Big Mac hamburgers in different countries.

Listed below in order are prices in dollars for a Big Mac hamburger in the United States, Canada, Mexico, China, Japan, Russia, Switzerland, Italy, Spain, Britain, India, and Egypt. Such data are used to compare currency exchange rates and the costs of goods in different countries. Find the range, variance, and standard deviation for the given sample data. What do the measures of variation tell us about the prices of a Big Mac in different countries? 5.30, 5.30, 2.56, 3.21, 3.38, 2.31, 6.80, 5.08, 4.80, 4.43, 2.81, 1.87 The variance is 2.28 dollars. The standard deviation is 1.51 dollars. What do the measures of variation tell us about the prices of a Big Mac in different countries? A. The variance and standard deviation tell us that Big Macs have lower prices in wealthier countries. B. The range alone tells us that there are very small differences among prices of Big Mac hamburgers in different countries. C. The variance and standard deviation tell us that Big Macs have higher prices in wealthier countries. D. The range alone tells us that there are very substantial differences among prices of Big Mac hamburgers in different countries.
Transcript text: Listed below in order are prices in dollars for a Big Mac hamburger in the United States, Canada, Mexico, China, Japan, Russia, Switzerland, Italy, Spain, Britain, India, and Egypt. Such data are used to compare currency exchange rates and the costs of goods in different countries. Find the range, variance, and standard deviation for the given sample data. What do the measures of variation tell us about the prices of a Big Mac in different countries? \[ \begin{array}{lllllllllllll} 5.30 & 5.30 & 2.56 & 3.21 & 3.38 & 2.31 & 6.80 & 5.08 & 4.80 & 4.43 & 2.81 & 1.87 & \text { 몬 } \end{array} \] The variance is 2.28 dollars ${ }^{2}$. The standard deviation is 1.51 dollars. What do the measures of variation tell us about the prices of a Big Mac in different countries? A. The variance and standard deviation tell us that Big Macs have lower prices in wealthier countries. B. The range alone tells us that there are very small differences among prices of Big Mac hamburgers in different countries. C. The variance and standard deviation tell us that Big Macs have higher prices in wealthier countries. D. The range alone tells us that there are very substantial differences among prices of Big Mac hamburgers in different countries.
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Solution

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Solution Steps

Step 1: Calculate the Range

The range of the Big Mac prices is calculated as follows:

\[ \text{Range} = \max(x_i) - \min(x_i) = 6.80 - 1.87 = 4.93 \]

Step 2: Calculate the Mean

The mean \( \mu \) of the prices is given by:

\[ \mu = \frac{\sum x_i}{n} = \frac{47.85}{12} \approx 3.99 \]

Step 3: Calculate the Variance

The variance \( \sigma^2 \) is calculated using the formula for sample variance:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} = 2.28 \]

Step 4: Calculate the Standard Deviation

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{2.28} \approx 1.51 \]

Step 5: Interpretation of Results

The measures of variation indicate that there are substantial differences among the prices of Big Mac hamburgers in different countries. Specifically, the range of \( 4.93 \) suggests significant variability in prices.

Final Answer

The results are summarized as follows:

  • Range: \( 4.93 \)
  • Variance: \( 2.28 \)
  • Standard Deviation: \( 1.51 \)

The interpretation leads us to conclude that the answer is:

\(\boxed{D}\)

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