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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 center of graph 1 is three places away from graph 2 and points are on average five away from the center in both graphs.
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.

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 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 seven places away from graph 2 and points are on average five away from the center in both graphs.

1 answer

Let's analyze the information given for both graphs:

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

  1. Distance Between Centers: 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 3 places away from the center of graph 2.

  2. Average Deviations: The average deviation (or the deviation) for both graphs is given as 5. This means that, on average, the points in both graphs are 5 units away from their respective centers.

Now let's review the response options:

  1. 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 statement is true.

  2. The two graphs have the same center and points are on average three away from the center. - This statement is false. The centers are not the same, and the deviations are 5, not 3.

  3. The center of graph 1 is five places away from graph 2 and points are on average 8.5 away from the center. - This statement is false. The centers are 3 places apart and the average deviation is 5.

  4. 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 statement is false. The centers are 3 places apart.

The correct response 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.