Please help!!
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.

data set 1 : the mean is (1+2+4+4+5+5+6+7+9+9+9+11) / 12 = 72/12 = 6

the MAD is :
1 - 6 = -5....|-5| = 5
2 - 6 = -4....|-4| = 4
4 - 6 = -2...|-2| = 2
4 - 6 = -2...|-2| = 2
5 - 6 = -1...|-1| = 1
5 - 6 = -1...|-1| = 1
6 - 6 = 0 ...| 0| = 0
7 - 6 = 1....|1| = 1
9 - 6 = 3...|3| = 3
9 - 6 = 3...|3| = 3
9 - 6 = 3...|3| = 3
11 - 6 = 5...|5| = 5

(5+4+2+2+1+1+0+1+3+3+3+5) / 12 = 30/12 = 2.5 <== the MAD

2nd data set :
the mean is (1+3+4+6+6+6+7+9+9+10+10+13) / 12 = 84/12 = 7

mad is :
1 - 7 = -6...| -6| = 6
3 - 7 = -4...|-4| = 4
4 - 7 = -3...|-3| = 3
6 - 7 = -1...|-1| = 1
6 - 7 = -1..|-1| = 1
6 - 7 = -1..|-1| = 1
7 - 7 = 0...|0| = 0
9 - 7 = 2...|2| = 2
9 - 7 = 2...|2| = 2
10 - 7 = 3..|3| = 3
10 - 7 = 3...|3| = 3
13 - 7 = 6...|6| = 6

(6+4+3+1+1+1+0+2+2+3+3+6) / 12 = 32/12 = 2.67 <== the MAD

the difference of the means is 1. This value is less then half of the mean absolute deviation of either data set. <== ur answer

akposevictor akposevictor · Answer 2 · 2022-06-29T14:35:51+02:00

The correct statements about the two data sets is: A. The difference of the means is 1. It is less than ½ of the mean absolute deviation of either data set.

How to Find the Mean Absolute Deviation?

List out each data points for each dot plot and find the mean, followed by the mean absolute deviation.

First dot plot has the following: 1, 2, 4, 4, 5, 5, 6, 7, 9, 9, 9, 11

Step 1: Find the mean of the data:

(1+2+4+4+5+5+6+7+9+9+9+11)/12 = 6

Step 2: Find the difference between each data and mean:

Difference between 1 and 6 is 5

Difference between 2 and 6 is 4

Difference between 4 and 6 is 2

Difference between 5 and 6 is 1

Difference between 6 and 6 is 0

Difference between 7 and 6 is 1

Difference between 9 and 6 is 3

Difference between 11 and 6 is 5

Step 3: Add all the differences:

5+4+2+2+1+1+0+1+3+3+3+5 = 30

Step 4: Divide it by the number of data:

30/12 = 2.5

Mean absolute deviation = 2.5

Second dot plot has the following: 1, 3, 4, 6, 6, 6, 7, 9, 9, 10, 10, 13

Step 1: Find the mean of the data:

(1+3+4+6+6+6+7+9+9+10+10+13)/12 = 7

Step 2: Find the difference between each data and mean:

Difference between 1 and 7 is 6

Difference between 3 and 7 is 4

Difference between 4 and 7 is 3

Difference between 6 and 7 is 1

Difference between 7 and 7 is 0

Difference between 9 and 7 is 2

Difference between 10 and 7 is 3

Difference between 13 and 7 is 6

Step 3: Add all the differences:

6+4+3+1+1+1+0+2+2+3+3+6 = 32

Step 4: Divide it by the number of data:

32/12 = 2.7

Mean absolute deviation = 2.7

Difference of their means = 7 - 6 = 1

1 is less than half of the mean absolute deviation of either data set. Therefore, the answer is: A.

Learn more about the mean absolute deviation on:

https://brainly.com/question/447169

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