The median absolute deviation, or MAD, is another measure of the spread of a dat
ID: 3203790 • Letter: T
Question
The median absolute deviation, or MAD, is another measure of the spread of a dataset. Here's how you find the MAD, given a dataset {x_i I = 1, n} Find the median q_0.5 Compute the quantities y_i = |x_i - q_0.5|, for i = 1.n. Defined this way, the y_i represent the magnitudes of the differences between the xi and the median. Order the y_i (in the notation from class, you'd be finding the {y_(i), i = 1, n} The median of the y_(i) is the MAD Given the dataset of 101 numbers {0, 1, 2, 3, ..., 97, 98, 99, 100} find the MAD Comment on how resistant of a measure the MAD is.Explanation / Answer
Numbers (N)
Sorted numbers(N)
Median (M)
Dev ( Di = |Ni - M|)
Sorted Di
Median (L)
0
0
50
50
50
25
1
1
49
49
2
2
48
48
3
3
47
47
4
4
46
46
5
5
45
45
6
6
44
44
7
7
43
43
8
8
42
42
9
9
41
41
10
10
40
40
11
11
39
39
12
12
38
38
13
13
37
37
14
14
36
36
15
15
35
35
16
16
34
34
17
17
33
33
18
18
32
32
19
19
31
31
20
20
30
30
21
21
29
29
22
22
28
28
23
23
27
27
24
24
26
26
25
25
25
25
26
26
24
24
27
27
23
23
28
28
22
22
29
29
21
21
30
30
20
20
31
31
19
19
32
32
18
18
33
33
17
17
34
34
16
16
35
35
15
15
36
36
14
14
37
37
13
13
38
38
12
12
39
39
11
11
40
40
10
10
41
41
9
9
42
42
8
8
43
43
7
7
44
44
6
6
45
45
5
5
46
46
4
4
47
47
3
3
48
48
2
2
49
49
1
1
50
50
0
0
51
51
1
1
52
52
2
2
53
53
3
3
54
54
4
4
55
55
5
5
56
56
6
6
57
57
7
7
58
58
8
8
59
59
9
9
60
60
10
10
61
61
11
11
62
62
12
12
63
63
13
13
64
64
14
14
65
65
15
15
66
66
16
16
67
67
17
17
68
68
18
18
69
69
19
19
70
70
20
20
71
71
21
21
72
72
22
22
73
73
23
23
74
74
24
24
75
75
25
25
76
76
26
26
77
77
27
27
78
78
28
28
79
79
29
29
80
80
30
30
81
81
31
31
82
82
32
32
83
83
33
33
84
84
34
34
85
85
35
35
86
86
36
36
87
87
37
37
88
88
38
38
89
89
39
39
90
90
40
40
91
91
41
41
92
92
42
42
93
93
43
43
94
94
44
44
95
95
45
45
96
96
46
46
97
97
47
47
98
98
48
48
99
99
49
49
100
100
50
50
Numbers (N)
Sorted numbers(N)
Median (M)
Dev ( Di = |Ni - M|)
Sorted Di
Median (L)
0
0
50
50
50
25
1
1
49
49
2
2
48
48
3
3
47
47
4
4
46
46
5
5
45
45
6
6
44
44
7
7
43
43
8
8
42
42
9
9
41
41
10
10
40
40
11
11
39
39
12
12
38
38
13
13
37
37
14
14
36
36
15
15
35
35
16
16
34
34
17
17
33
33
18
18
32
32
19
19
31
31
20
20
30
30
21
21
29
29
22
22
28
28
23
23
27
27
24
24
26
26
25
25
25
25
26
26
24
24
27
27
23
23
28
28
22
22
29
29
21
21
30
30
20
20
31
31
19
19
32
32
18
18
33
33
17
17
34
34
16
16
35
35
15
15
36
36
14
14
37
37
13
13
38
38
12
12
39
39
11
11
40
40
10
10
41
41
9
9
42
42
8
8
43
43
7
7
44
44
6
6
45
45
5
5
46
46
4
4
47
47
3
3
48
48
2
2
49
49
1
1
50
50
0
0
51
51
1
1
52
52
2
2
53
53
3
3
54
54
4
4
55
55
5
5
56
56
6
6
57
57
7
7
58
58
8
8
59
59
9
9
60
60
10
10
61
61
11
11
62
62
12
12
63
63
13
13
64
64
14
14
65
65
15
15
66
66
16
16
67
67
17
17
68
68
18
18
69
69
19
19
70
70
20
20
71
71
21
21
72
72
22
22
73
73
23
23
74
74
24
24
75
75
25
25
76
76
26
26
77
77
27
27
78
78
28
28
79
79
29
29
80
80
30
30
81
81
31
31
82
82
32
32
83
83
33
33
84
84
34
34
85
85
35
35
86
86
36
36
87
87
37
37
88
88
38
38
89
89
39
39
90
90
40
40
91
91
41
41
92
92
42
42
93
93
43
43
94
94
44
44
95
95
45
45
96
96
46
46
97
97
47
47
98
98
48
48
99
99
49
49
100
100
50
50
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