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Given the following descriptions, which of the following correctly compares the average deviations and describes how the center of graph 1 relates to that of graph 2? graph 1: mean=7; deviation=5 graph 2: mean=10; deviation=5 (1 point) Responses The two graphs have the same center and points are on average three away from the center. The two graphs have the same center and points are on average three away from the center. 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. 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. The center of graph 1 is five places away from graph 2 and points are on average 8.5 away from the center. The center of graph 1 is five places away from graph 2 and points are on average 8.5 away from the center. 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.

1 answer

To compare the two graphs, we examine their means and deviations:

  • Graph 1: Mean = 7; Deviation = 5
  • Graph 2: Mean = 10; Deviation = 5

Centers of the two graphs:

  • The mean of Graph 1 is 7.
  • The mean of Graph 2 is 10.
  • The difference (distance) between the two means: \( |10 - 7| = 3 \).

Average deviations:

  • The deviation for Graph 1 is 5, meaning points are, on average, 5 units away from the mean of 7.
  • The deviation for Graph 2 is also 5, meaning points are, on average, 5 units away from the mean of 10.

With this analysis, we can evaluate the responses:

  1. The two graphs have the same center and points are on average three away from the center.

    • Incorrect: They do not have the same center (7 vs. 10).

  2. 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.

    • Incorrect: The centers are 3 places apart, not 7.

  3. The center of graph 1 is five places away from graph 2 and points are on average 8.5 away from the center.

    • Incorrect: The centers are 3 places apart, and the average distance from the mean is 5, not 8.5.

  4. 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.

    • Correct: The centers are indeed 3 apart, and the average deviation for both is 5.

  5. 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 appears to be a repeat of the previous response and is still correct.

Thus, the correct comparison and description 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.