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Dmitriy789 [7]
3 years ago
7

Which pair of statements correctly compares the two data sets?

Mathematics
2 answers:
Vika [28.1K]3 years ago
5 0
As a rule option A is the answer to a degree
olga2289 [7]3 years ago
4 0

Answer:

<h2>A. The difference of the means is 1. This value is less than half of the mean absolute deviation of either data set.</h2>

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.

<h3>Blue data set.</h3>

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

<h3>Green data set.</h3>

\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.

<h3>Blue data set.</h3>

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

<h3>Green data set.</h3>

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.

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