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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 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 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.

1 answer

To analyze the two graphs based on the provided information:

  • Graph 1 has a mean of 7 and a deviation of 5.
  • Graph 2 has a mean of 10 and a deviation of 5.

Now, let's break this down:

  1. Mean of Graph 1: 7
  2. Mean of Graph 2: 10

To find the distance between the centers of the two graphs (mean values):

  • Distance = Mean of Graph 2 - Mean of Graph 1 = 10 - 7 = 3.

This indicates that the center of Graph 1 is 3 places away from the center of Graph 2.

  1. Average Deviation: Both graphs have a deviation of 5, which means that, on average, the data points in both graphs are 5 units away from their respective centers.

Using this information, we can evaluate the responses:

  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 correct.)

  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. (This statement is incorrect as the centers are actually three places apart, not seven.)

  3. The two graphs have the same center and points are on average three away from the center. (This statement is incorrect as the graphs have different centers.)

  4. 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 incorrect as the distance is three places, not five, and the average deviation is five, not 8.5.)

Thus, 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.