Question

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? 5.26 5.30 2.61 3.19 3.40 2.32 6.78 5.09 4.81 4.37 2.80 1.85 the range is 4.93 dollars. (type an integer or decimal rounded to two decimal places as needed.) the variance is 2.26 dollars^2. (type an integer or decimal rounded to two decimal places as needed.) the standard deviation is (type an integer or decimal ro l places as needed.) dollars^2 dollars

Explanation:

Step1: <Calculate the mean>

First, find the sum of the data: \(5.26 + 5.30+2.61 + 3.19+3.40+2.32 + 6.78+5.09+4.81+4.37+2.80+1.85=\sum x = 47.88\).
The number of data points \(n = 12\).
The mean \(\bar{x}=\frac{\sum x}{n}=\frac{47.88}{12}=3.99\).

Step2: <Calculate the variance>

The formula for the sample variance \(s^{2}=\frac{\sum(x - \bar{x})^{2}}{n - 1}\).
\((5.26-3.99)^{2}=1.27^{2}=1.6129\), \((5.30 - 3.99)^{2}=1.31^{2}=1.7161\), \((2.61-3.99)^{2}=(-1.38)^{2}=1.9044\), \((3.19-3.99)^{2}=(-0.8)^{2}=0.64\), \((3.40 - 3.99)^{2}=(-0.59)^{2}=0.3481\), \((2.32-3.99)^{2}=(-1.67)^{2}=2.7889\), \((6.78-3.99)^{2}=2.79^{2}=7.7841\), \((5.09-3.99)^{2}=1.1^{2}=1.21\), \((4.81-3.99)^{2}=0.82^{2}=0.6724\), \((4.37-3.99)^{2}=0.38^{2}=0.1444\), \((2.80-3.99)^{2}=(-1.19)^{2}=1.4161\), \((1.85 - 3.99)^{2}=(-2.14)^{2}=4.5796\).
\(\sum(x - \bar{x})^{2}=1.6129+1.7161 + 1.9044+0.64+0.3481+2.7889+7.7841+1.21+0.6724+0.1444+1.4161+4.5796=24.837\).
\(s^{2}=\frac{24.837}{12 - 1}=\frac{24.837}{11}\approx2.26\).

Step3: <Calculate the standard deviation>

The formula for the sample standard deviation \(s=\sqrt{s^{2}}\).
Since \(s^{2}\approx2.26\), then \(s=\sqrt{2.26}\approx1.50\).

Answer:

The standard deviation is \(1.50\) dollars.