Listed below in order are prices in dollars for a Big Mac hamburger in the 

United StatesUnited States​, 

CanadaCanada​, 

MexicoMexico​, 

ChinaChina​, 

JapanJapan​, 

RussiaRussia​, 

SwitzerlandSwitzerland​, 

ItalyItaly​, 

SpainSpain​, 

BritainBritain​, 

IndiaIndia​, 

and 

EgyptEgypt. 

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?Country	Price

United States	5.27

Canada	5.27

Mexico	2.59

China	3.23

Japan	3.36

Russia	2.30

Switzerland	6.82

Italy	5.09

Spain	4.84

Britain	4.40

India	2.82

Egypt	1.93The range is 

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dollars squared .dollars2.

dollars.dollars.

​(Type an integer or decimal rounded to two decimal places as​ needed.)


To find the range, variance, and standard deviation of the given sample data, we will follow these steps:

### 1. Range
The range is the difference between the maximum and minimum values in the dataset.

\[
\text{Range} = \text{Maximum value} - \text{Minimum value}
\]

From the given dataTo find the range, variance, and standard deviation of the given sample data, we will follow these steps:

### 1. Range
The range is the difference between the maximum and minimum values in the dataset.

\[
\text{Range} = \text{Maximum value} - \text{Minimum value}
\]

From the given 

- Maximum value: 6.82 (Switzerland)
- Minimum value: 1.93 (Egypt)

\[
\text{Range} = 6.82 - 1.93 = 4.89
\]

### 2. Variance and Standard Deviation
First, we need to calculate the mean ($\bar{x}$):

\[
\bar{x} = \frac{\sum x}{n}
\]

where $n$ is the number of data points.

List of prices:

\[
5.27, 5.27, 2.59, 3.23, 3.36, 2.30, 6.82, 5.09, 4.84, 4.40, 2.82, 1.93
\]

Sum of prices:

\[
5.27 + 5.27 + 2.59 + 3.23 + 3.36 + 2.30 + 6.82 + 5.09 + 4.84 + 4.40 + 2.82 + 1.93 = 47.92
\]

Number of data points ($n$):

\[
n = 12
\]

Mean ($\bar{x}$):

\[
\bar{x} = \frac{47.92}{12} \approx 3.9933
\]

Next, calculate the variance ($s^2$) using the formula:

\[
s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}
\]

First, compute each squared deviation from the mean and sum them:

\[
\begin{aligned}
(5.27 - 3.9933)^2 & \approx 1.6261, \\
(5.27 - 3.9933)^2 & \approx 1.6261, \\
(2.59 - 3.9933)^2 & \approx 1.9823, \\
(3.23 - 3.9933)^2 & \approx 0.5843, \\
(3.36 - 3.9933)^2 & \approx 0.4001, \\
(2.30 - 3.9933)^2 & \approx 2.8652, \\
(6.82 - 3.9933)^2 & \approx 7.9706, \\
(5.09 - 3.9933)^2 & \approx 1.1971, \\
(4.84 - 3.9933)^2 & \approx 0.7162, \\
(4.40 - 3.9933)^2 & \approx 0.1652, \\
(2.82 - 3.9933)^2 & \approx 1.3781, \\
(1.93 - 3.9933)^2 & \approx 4.2581
\end{aligned}
\]

Sum of squared deviations:

\[
1.6261 + 1.6261 + 1.9823 + 0.5843 + 0.4001 + 2.8652 + 7.9706 + 1.1971 + 0.7162 + 0.1652 + 1.3781 + 4.2581 = 22.7694
\]

Variance ($s^2$):

\[
s^2 = \frac{22.7694}{11} \approx 2.0708
\]

Standard deviation ($s$):

\[
s = \sqrt{2.0708} \approx 1.4397
\]

### Summary
- **Range**: $4.89$ dollars
- **Variance**: $2.0708$ dollars$^2$
- **Standard Deviation**: $1.4397$ dollars

### Interpretation
The measures of variation (range, variance, and standard deviation) indicate that there is a noticeable spread in the prices of a Big Mac across different countries. The range shows a difference of $4.89 between the highest and lowest prices, while the standard deviation and variance provide insights into how much the prices deviate from the mean price on average. This variability can be attributed to differences in currency exchange rates, cost of living, and local economic conditions.

Do you want more details or have any questions?

Here are some related questions you might ask:

1. How does the standard deviation help in understanding data dispersion?
2. What other measures of central tendency can be useful for this data set?
3. How would the results change if we considered more countries?
4. Can you explain the concept of skewness in this context?
5. What is the significance of using variance instead of standard deviation?

**Tip:** Always ensure you use the same units (dollars, in this case) consistently throughout your calculations to maintain accuracy.

Learn how to calculate the range, variance, and standard deviation of Big Mac prices in various countries including the United States, Canada, Mexico, China, Japan, Russia, Switzerland, Italy, Spain, Britain, India, and Egypt. Understand the measures of variation and what they reveal about price differences.

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