To compare the averages and deviations of the two graphs based on the provided descriptions, we can analyze the information given:
- Graph 1: Mean = 7, Deviation = 5
- Graph 2: Mean = 10, Deviation = 5
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Comparing the Centers (Means):
- The mean of Graph 1 is 7, and the mean of Graph 2 is 10.
- The distance between the two means is: 10 - 7 = 3.
- So, the center of graph 1 is three places away from graph 2.
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Comparing the Deviations:
- The average deviation (or standard deviation) for both graphs is 5. This means that on average, data points in both graphs are 5 units away from their respective means.
Now, let’s analyze the given response options:
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"(incorrect): The center of graph 1 is five places away from graph 2 and points are on average 8.5 away from the center."
- This is incorrect because the distance between the centers is 3, not 5, and the average deviations are both 5, not 8.5.
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"(correct): The center of graph 1 is three places away from graph 2 and points are on average five away from the center in both graphs."
- This is correct! The centers are 3 apart, and the deviations are both 5.
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"(incorrect): The two graphs have the same center and points are on average three away from the center."
- This is incorrect because the means are not the same.
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"(incorrect): The center of graph 1 is seven places away from graph 2 and points are on average five away from the center in both graphs."
- This is incorrect because the centers are not 7 apart; they are 3 apart.
Therefore, the correct response that accurately describes the comparison is:
The center of graph 1 is three places away from graph 2 and points are on average five away from the center in both graphs.