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