listed below in order are prices (in dollars) for a big mac hamburger in the united states, canada, mexico, china, japan, greece, 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 5.39 2.61 3.19 3.40 2.52 6.76 5.09 4.81 4.37 2.80 1.85
the range is 4.91 dollars
(type an integer or decimal rounded to two decimal places as needed.)
the variance is 2.26 dollars²
(type an integer or decimal rounded to two decimal places as needed.)
the standard deviation is 1.50 dollars
(type an integer or decimal rounded to two decimal places as needed.)
what do the measures of variation tell us about the prices of a big mac in different countries?
oa. the variance and standard deviation tell us that big macs have lower prices in wealthier countries.
ob. the variance and standard deviation tell us that big macs have higher prices in wealthier countries.
oc. the range alone tells us that there are very substantial differences among prices of big mac hamburgers in different countries.
od. the range alone tells us that there are very small differences among prices of big mac hamburgers in different countries.

Question

Accepted Answer

# Explanation:
## Step1: Calculate the range
The range is the difference between the maximum and minimum values.
The maximum value is $6.76$, the minimum value is $1.85$.
$Range=6.76 - 1.85=4.91$
## Step2: Calculate the mean $\bar{x}$
$\bar{x}=\frac{5.26 + 5.39+2.61+3.99+3.40+2.52+6.76+5.09+4.81+4.37+2.80+1.85}{12}$
$\bar{x}=\frac{50.9}{12}\approx4.24$
## Step3: Calculate the variance $s^{2}$
$$
\begin{align*}
s^{2}&=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\
&=\frac{(5.26-4.24)^{2}+(5.39 - 4.24)^{2}+(2.61-4.24)^{2}+(3.99-4.24)^{2}+(3.40-4.24)^{2}+(2.52-4.24)^{2}+(6.76-4.24)^{2}+(5.09-4.24)^{2}+(4.81-4.24)^{2}+(4.37-4.24)^{2}+(2.80-4.24)^{2}+(1.85-4.24)^{2}}{11}\
&=\frac{(1.02)^{2}+(1.15)^{2}+(-1.63)^{2}+(-0.25)^{2}+(-0.84)^{2}+(-1.72)^{2}+(2.52)^{2}+(0.85)^{2}+(0.57)^{2}+(0.13)^{2}+(-1.44)^{2}+(-2.39)^{2}}{11}\
&=\frac{1.0404+1.3225 + 2.6569+0.0625+0.7056+2.9584+6.3504+0.7225+0.3249+0.0169+2.0736+5.7121}{11}\
&=\frac{24.9467}{11}\approx2.27
\end{align*}
$$
## Step4: Calculate the standard deviation $s$
$s=\sqrt{s^{2}}=\sqrt{2.27}\approx1.51$
## Step5: Analyze the measures of variation
The range is $4.91$, which is relatively large. This indicates that there are substantial differences among the prices of Big - Mac hamburgers in different countries.

# Answer:
The range is $4.91$ dollars.
The variance is $2.27$ dollars².
The standard deviation is $1.51$ dollars.
For the multiple - choice question: C. The range alone tells us that there are very substantial differences among prices of Big Mac hamburgers in different countries.

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the range

Step2: Calculate the mean \(\bar{x}\)

Step3: Calculate the variance \(s^{2}\)

Step4: Calculate the standard deviation \(s\)

Step5: Analyze the measures of variation

Answer: