Question

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 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. 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.

Answer 1

To analyze the information provided:

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

First, let's compare the means of the two graphs:

• The difference between the means of Graph 1 and Graph 2 is: \(10 - 7 = 3\). So, the centers of Graph 1 and Graph 2 are 3 units apart.

Next, regarding the average deviations:

• Both graphs have the same average deviation of 5, meaning on average, the data points in each graph deviate 5 units from their respective means.

Now we can eliminate the incorrect options based on our analysis:

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 based on our analysis.
2. "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 distance is 3, not 5, and the average deviation is not 8.5.
3. "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 due to the distance being 3 not 7.
4. "The two graphs have the same center and points are on average three away from the center." - Incorrect, as the centers are not the same.

Therefore, 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.