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? the range is 4.9 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 1.5 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? a. the range alone tells us that there are very substantial differences among prices of big mac hamburgers in different countries. b. the range alone tells us that there are very small differences among prices of big mac hamburgers in different countries. c. the variance and standard deviation tell us that big macs have higher prices in wealthier countries. d. the variance and standard deviation tell us that big macs have lower prices in wealthier countries.

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# Brief Explanations:
To determine the correct option, we analyze the measures of variation (range, variance, standard deviation) and their interpretation. The range is 4.9, variance is 2.26, and standard deviation is 1.5. These values indicate the spread of the data. Option A claims "substantial differences" but the standard deviation (1.5) and variance (2.26) suggest a moderate spread, not extremely large. Option B says "very small differences" which is incorrect as the range is 4.9 (not small). Options C and D make claims about wealthier countries, but the measures of variation (range, variance, standard deviation) only tell us about the spread of prices, not about the relationship with a country's wealth. Wait, re - evaluating: The range is 6.81 - 1.91 = 4.9, variance 2.26, standard deviation ~1.5. The key is that the measures of variation (range, variance, std dev) describe the dispersion of the data. Option B says "very small differences" – but a range of 4.9 and std dev of 1.5 is not very small. Option A: "substantial" – maybe? Wait, no, the question is about what the measures tell us. Wait, the options: A says range alone tells substantial differences. But range is a simple measure, but the variance and std dev also. Wait, the question is "What do the measures of variation tell us about the prices...". The measures of variation (range, variance, standard deviation) tell us about the spread (how much the prices differ from each other). Option B: "very small differences" – no, because range is 4.9, which is not very small. Option A: "substantial differences" – the range is 4.9, variance 2.26, std dev 1.5. So there are differences. But wait, maybe the correct answer is B? No, wait, let's check the data: the prices are 5.31, 5.29, 2.62, 3.22, 3.39, 2.29, 6.81, 5.06, 4.78, 4.39, 2.76, 1.91. The minimum is 1.91, maximum is 6.81, so range 4.9. The variance is 2.26, std dev 1.5. So the prices do have some differences, but are they "substantial"? Or "very small"? A range of 4.9 in dollar prices for a Big Mac – that's a noticeable difference. But the options: A: range alone tells substantial differences. B: range alone tells very small differences. C: variance and std dev tell higher prices in wealthier. D: lower in wealthier. But the measures of variation don't tell us about wealth, only about the spread. Wait, maybe I misread. Wait, the question is "What do the measures of variation tell us about the prices of a Big Mac in different countries?". The measures of variation (range, variance, standard deviation) describe the dispersion (how spread out the prices are). So if the range is 4.9, variance 2.26, std dev 1.5, that means there are differences. But option B says "very small differences" – that's wrong. Option A says "substantial differences" – maybe. But wait, maybe the correct answer is B? No, 4.9 range is not very small. Wait, maybe the answer is B? No, let's think again. Wait, the data points: let's list them: 1.91, 2.29, 2.62, 2.76, 3.22, 3.39, 4.39, 4.78, 5.06, 5.29, 5.31, 6.81. The range is 6.81 - 1.91 = 4.9. The variance is 2.26, std dev 1.5. So the prices are spread out, but not extremely. But the options: A: "substantial differences" – maybe. B: "very small differences" – no. C and D talk about wealth, which the measures of variation don't indicate. So between A and B, A is more correct because the range is 4.9 (not very small) so there are substantial differences? Wait, maybe the answer is B? No, I think I made a mistake. Wait, the question is about what the measures tell us. The range alone: range is max - min. So 6.81 - 1.91 = 4.9. So the range tells us the difference between the highest and lowest. So if the range is 4.9, that's a noticeable difference, so "substantial" (option A) or "very small" (option B). 4.9 dollars difference is not very small, so A is correct? Wait, but maybe the answer is B? No, I think A is correct. Wait, but let's check the options again. Option A: "The range alone tells us that there are very substantial differences among prices...". Option B: "The range alone tells us that there are very small differences...". Since range is 4.9, which is a significant difference (e.g., from ~2 to ~7 dollars), so A is correct. But wait, maybe the intended answer is B? No, I think A. Wait, no, maybe I messed up. Wait, the variance is 2.26, std dev 1.5. So the standard deviation is 1.5, which is a moderate spread. But the range is 4.9. So the range shows a larger spread, but variance and std dev show a moderate one. But the question is about what the measures (range, variance, std dev) tell us. So the correct option should be about the spread. Option B says "very small differences" – incorrect. Option A says "substantial differences" – more correct. But wait, maybe the answer is B? No, I think A. Wait, but let's see the data: the prices are from ~2 to ~7, so differences of up to ~5 dollars. So that's substantial. So the answer is A.
# Answer:
A. The range alone tells us that there are very substantial differences among prices of Big Mac hamburgers in different countries.

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