Ita are used to compare currency exchange rates and the costs of goods in different countries. Fin for the given sample data. What do the measures of variation tell us about the prices of a Big Mac in different col 5.29 2.55 3.20 3.42 2.29 6.78 5.12 4.83 4.42 2.78 1.92 integer or decimal rounded to two decimal places as needed.) ard deviation is nteger or decimal rounded to two decimal places as needed.) he measures of variation tell us about the prices of a Big Mac in different countries? e range alone tells us that there are very small differences among prices of Big Mac hamburgers in different co e variance and standard deviation tell us that Big Macs have higher prices in wealthier countries.
Ita are used to compare currency exchange rates and the costs of goods in different countries. Fin for the given sample data. What do the measures of variation tell us about the prices of a Big Mac in different col 5.29 2.55 3.20 3.42 2.29 6.78 5.12 4.83 4.42 2.78 1.92 integer or decimal rounded to two decimal places as needed.) ard deviation is nteger or decimal rounded to two decimal places as needed.) he measures of variation tell us about the prices of a Big Mac in different countries? e range alone tells us that there are very small differences among prices of Big Mac hamburgers in different co e variance and standard deviation tell us that Big Macs have higher prices in wealthier countries.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question 13
![### Big Mac Prices Around the World
**Introduction:**
Analyzing the cost of a Big Mac hamburger in various countries can provide insights into currency exchange rates and the cost of goods in different regions. The data presented below showcases the prices in US dollars of a Big Mac across multiple countries including the United States, Canada, Mexico, China, Japan, Russia, Switzerland, Italy, Spain, Britain, India, and Egypt. The following measures of variation will be calculated: range, variance, and standard deviation.
**Price Data (in USD):**
- United States: $5.27
- Canada: $5.29
- Mexico: $2.55
- China: $3.20
- Japan: $3.42
- Russia: $2.29
- Switzerland: $6.78
- Italy: $5.12
- Spain: $4.83
- Britain: $4.22
- India: $2.78
- Egypt: $1.92
**Measures of Variation:**
1. **Range:**
- The range is the difference between the maximum and minimum values in a data set.
- \[
\text{Range} = \text{Maximum Price} - \text{Minimum Price}
\]
- Range: [Enter the calculated value rounded to two decimal places]
2. **Variance:**
- Variance measures how much the values in the data set differ from the mean (average).
- \[
\text{Variance} = \frac{\sum (x_i - \mu)^2}{N}
\]
- Variance: [Enter the calculated value rounded to two decimal places]
3. **Standard Deviation:**
- Standard deviation is the square root of the variance and provides a measure of the spread of values around the mean.
- \[
\text{Standard Deviation} = \sqrt{\text{Variance}}
\]
- Standard Deviation: [Enter the calculated value rounded to two decimal places]
**Analysis:**
What do these measures of variation tell us about the prices of a Big Mac in different countries?
- **Option A:**
The range alone tells us that there are very small differences among prices of Big Mac hamburgers in different countries.
**Graphical Representation:**
No graphical representation is provided for this data. However, students are encouraged to plot the data on a](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a767b23-c124-4e33-a8c8-1cb736a4d72e%2F1bdfbf3a-8612-45fc-9c5f-823b89d6c723%2Fowbpni_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Big Mac Prices Around the World
**Introduction:**
Analyzing the cost of a Big Mac hamburger in various countries can provide insights into currency exchange rates and the cost of goods in different regions. The data presented below showcases the prices in US dollars of a Big Mac across multiple countries including the United States, Canada, Mexico, China, Japan, Russia, Switzerland, Italy, Spain, Britain, India, and Egypt. The following measures of variation will be calculated: range, variance, and standard deviation.
**Price Data (in USD):**
- United States: $5.27
- Canada: $5.29
- Mexico: $2.55
- China: $3.20
- Japan: $3.42
- Russia: $2.29
- Switzerland: $6.78
- Italy: $5.12
- Spain: $4.83
- Britain: $4.22
- India: $2.78
- Egypt: $1.92
**Measures of Variation:**
1. **Range:**
- The range is the difference between the maximum and minimum values in a data set.
- \[
\text{Range} = \text{Maximum Price} - \text{Minimum Price}
\]
- Range: [Enter the calculated value rounded to two decimal places]
2. **Variance:**
- Variance measures how much the values in the data set differ from the mean (average).
- \[
\text{Variance} = \frac{\sum (x_i - \mu)^2}{N}
\]
- Variance: [Enter the calculated value rounded to two decimal places]
3. **Standard Deviation:**
- Standard deviation is the square root of the variance and provides a measure of the spread of values around the mean.
- \[
\text{Standard Deviation} = \sqrt{\text{Variance}}
\]
- Standard Deviation: [Enter the calculated value rounded to two decimal places]
**Analysis:**
What do these measures of variation tell us about the prices of a Big Mac in different countries?
- **Option A:**
The range alone tells us that there are very small differences among prices of Big Mac hamburgers in different countries.
**Graphical Representation:**
No graphical representation is provided for this data. However, students are encouraged to plot the data on a
![### Analysis of Big Mac Prices Across Various Countries
**Objective:**
Understand how currency exchange rates and the cost of goods vary across different countries by examining the price of a Big Mac.
**Given Data:**
Prices of a Big Mac hamburger in various countries (in USD):
- **United States:** $5.27
- **Canada:** $5.29
- **Mexico:** $2.55
- **China:** $3.20
- **Japan:** $3.42
- **Russia:** $2.29
- **Switzerland:** $6.78
- **Italy:** $5.12
- **Spain:** $4.83
- **Britain:** $4.42
- **India:** $2.78
- **Egypt:** $1.92
**Task:**
Find the range, variance, and standard deviation for the given prices, and interpret the measures of variation in terms of pricing differences for Big Macs in different countries.
#### Calculations:
1. **Range:**
The range is the difference between the maximum and minimum price.
\[
\text{Range} = \text{Max} - \text{Min} = 6.78 - 1.92 = 4.86
\]
2. **Standard Deviation:**
(Calculation involves finding the mean and then the variance, which is the average of the squared differences from the mean, followed by taking the square root of the variance to find the standard deviation.)
*Let's suppose the standard deviation is calculated and given.*
3. **Interpretation of Measures of Variation:**
**What do the measures of variation tell us about the prices of a Big Mac in different countries?**
___Options:___
- **A.** The range alone tells us that there are very small differences among prices of Big Mac hamburgers in different countries.
- **B.** The variance and standard deviation tell us that Big Macs have higher prices in wealthier countries.
- **C.** The range alone tells us that there are very substantial differences among prices of Big Mac hamburgers in different countries.
- **D.** The variance and standard deviation tell us that Big Macs have lower prices in wealthier countries.
**Correct Interpretation:**
**C.** The range alone tells us that there are very substantial differences among prices of Big Mac hamburgers in different](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a767b23-c124-4e33-a8c8-1cb736a4d72e%2F1bdfbf3a-8612-45fc-9c5f-823b89d6c723%2F2y599ff_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Analysis of Big Mac Prices Across Various Countries
**Objective:**
Understand how currency exchange rates and the cost of goods vary across different countries by examining the price of a Big Mac.
**Given Data:**
Prices of a Big Mac hamburger in various countries (in USD):
- **United States:** $5.27
- **Canada:** $5.29
- **Mexico:** $2.55
- **China:** $3.20
- **Japan:** $3.42
- **Russia:** $2.29
- **Switzerland:** $6.78
- **Italy:** $5.12
- **Spain:** $4.83
- **Britain:** $4.42
- **India:** $2.78
- **Egypt:** $1.92
**Task:**
Find the range, variance, and standard deviation for the given prices, and interpret the measures of variation in terms of pricing differences for Big Macs in different countries.
#### Calculations:
1. **Range:**
The range is the difference between the maximum and minimum price.
\[
\text{Range} = \text{Max} - \text{Min} = 6.78 - 1.92 = 4.86
\]
2. **Standard Deviation:**
(Calculation involves finding the mean and then the variance, which is the average of the squared differences from the mean, followed by taking the square root of the variance to find the standard deviation.)
*Let's suppose the standard deviation is calculated and given.*
3. **Interpretation of Measures of Variation:**
**What do the measures of variation tell us about the prices of a Big Mac in different countries?**
___Options:___
- **A.** The range alone tells us that there are very small differences among prices of Big Mac hamburgers in different countries.
- **B.** The variance and standard deviation tell us that Big Macs have higher prices in wealthier countries.
- **C.** The range alone tells us that there are very substantial differences among prices of Big Mac hamburgers in different countries.
- **D.** The variance and standard deviation tell us that Big Macs have lower prices in wealthier countries.
**Correct Interpretation:**
**C.** The range alone tells us that there are very substantial differences among prices of Big Mac hamburgers in different
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