tion from the Mean Quick Check

Question

3 of 53 of 5 Items

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 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 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.

Answer 1

To analyze the relationship between the two graphs, let's look at the provided information:

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

1. Comparison of Means (Centers):

   • Mean of Graph 1: 7
   • Mean of Graph 2: 10
   • The difference between the two means:
     \(10 - 7 = 3\)
     Therefore, the center of Graph 1 is 3 units away from the center of Graph 2.

2. Comparison of Deviations:

   • The average 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 means.

Now let's analyze the provided response options:

1. First option:

   • "The two graphs have the same center and points are on average three away from the center."
   • This is incorrect because the centers are different.

2. Second option:

   • "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 average deviations are 5, not 8.5.

3. Third option:

   • "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 as it accurately describes the centers and the deviations.

4. Fourth option:

   • "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 distance between the centers is 3, not 7.

Based on the analysis, the correct 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.

The correct response is the third option.