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?
5.29
5.29
2.62
3.18
3.39
2.30
6.79
5.08
4.83
4.39
2.82
1.90

The calculations for the given Big Mac prices across different countries are as follows:

- **Range**: \$4.89  
- **Variance**: 2.25  
- **Standard deviation**: 1.50  

### Interpretation of the measures of variation:
- The **range** of \$4.89 indicates that there is a significant difference in Big Mac prices across the sampled countries.
- The **variance** of 2.25 and the **standard deviation** of 1.50 suggest that the prices of Big Macs in different countries vary moderately. Some countries have prices significantly lower or higher than the average.

Would you like further details on this, or do you have any questions?

Here are 5 related questions to deepen understanding:
1. What is the average price of a Big Mac in these countries?
2. How do currency exchange rates affect the price variations of the Big Mac globally?
3. Can you calculate the median price of the Big Mac for the given data?
4. How would adding more countries to this dataset affect the standard deviation?
5. How do factors like purchasing power parity (PPP) explain the difference in Big Mac prices?

**Tip:** A large standard deviation means the data points are spread out over a wider range of values.

Analyze Big Mac prices from 12 different countries with a detailed breakdown of range, variance, and standard deviation. This problem demonstrates key concepts in statistics, such as measures of dispersion and variation, helping students understand global price differences. Suitable for Grades 10-12.

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