Question

Which pair of statements correctly compares the two data sets?

Answer 1

As a rule option A is the answer to a degree

Answer 2

Answer:

A. The difference of the means is 1. This value is less than half of the mean absolute deviation of either data set.

Step-by-step explanation:

The mean absolute deviation is defined by

$MAD=\frac{\sum (x- \mu)}{N}$

Where $\mu$ is the mean and $N$ is the total number of elements.

First, we find each mean.

Blue data set.

$\mu_{blue} = \frac{1+2+4+4+5+5+6+7+9+9+9+11}{12} =\frac{72}{12}= 6$

Green data set.

$\mu_{green}=\frac{1+3+4+6+6+6+7+9+9+10+10+13}{12}= \frac{84}{12}=7$

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

Now, let's find each MAD.

Blue data set.

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,

$MAD=\frac{30}{12}=2.5$

Green data set.

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,

$MAD=\frac{32}{12} \approx 2.67$

Notice that half of each mean is greater than one.

Therefore, the choice A is correct.