Answer:
Step-by-step explanation:
The mean absolute deviation is defined by
[tex]MAD=\frac{\sum (x- \mu)}{N}[/tex]
Where [tex]\mu[/tex] is the mean and [tex]N[/tex] is the total number of elements.
First, we find each mean.
[tex]\mu_{blue} = \frac{1+2+4+4+5+5+6+7+9+9+9+11}{12} =\frac{72}{12}= 6[/tex]
[tex]\mu_{green}=\frac{1+3+4+6+6+6+7+9+9+10+10+13}{12}= \frac{84}{12}=7[/tex]
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,
[tex]MAD=\frac{30}{12}=2.5[/tex]
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,
[tex]MAD=\frac{32}{12} \approx 2.67[/tex]
Notice that half of each mean is greater than one.
Therefore, the choice A is correct.
