Which pair of statements correctly compares the two data sets?

a. the difference of the means is 1. this value is less than half of the mean absolute deviation of either data set.
b. the difference of the means is 1. this value is more than half of the mean absolute deviation of either data set.
c. the difference of the means is 1. this value is 1 times the mean absolute deviation of either data set.
d. the difference of the means is 1. this value is 2 times the mean absolute deviation of either data set.

Step-by-step explanation:

The mean absolute deviation is defined by

Where is the mean and is the total number of elements.

First, we find each mean.

As you can observe, they have a difference of 1 unit regarding their means.

Now, let's find each MAD.

First, we find the difference between the mean and each data, to then sum all differences.

1 - 6 = |-5|

2 - 6 = |-4|

4 - 6 =|-2|

4 - 6 = |-2|

5 - 6 = |-1|

5 - 6 =|-1|

6 - 6 = 0

7 - 6 = |1|

9 - 6 = |3|

9 - 6 = |3|

9 - 6 =| 3|

11 - 6 =| 5|

Which gives a total of 30.

Then,

We repeat the process.

1 - 7 = |-6|

3 - 7 =|-4|

4 - 7 = |-3|

6 - 7 = |-1|

6 - 7 = |-1|

6 - 7 =| -1|

7 - 7 = 0

9 - 7 = |2|

9 - 7 = |2|

10 - 7 =| 3|

10 - 7 = |3|

13 - 7 =|6|

Which gives a total of 32.

Then,

Notice that half of each mean is greater than one.

Therefore, the choice A is correct.

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