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 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.
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 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.

1 answer

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
  1. 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.
  2. 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:

  1. "(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.
  2. "(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.
  3. "(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.
  4. "(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.