The four tables below shows the data interpretation for the exponents of the first four primes (2, 3, 5, 7) that they appear in the known multiply perfect numbers. I use the 4 common measures of statistics:
- Mean: The sum of all data values divided by the number of data values
- Median: The middle data value in an ordered set of data
- Mode: The number that occurs the most often in a set of data
- Standard deviation: Measures the dispersion of a data set around the mean (data below uses population standard deviation)
Data for exponents of 2
edit
Abundancy
|
Mean
|
Median
|
Mode
|
Standard deviation
|
2
|
11376955.90196
|
23208
|
—
|
21707346.80098
|
3
|
8.66667
|
8.5
|
—
|
3.94405
|
4
|
16.91667
|
14
|
25
|
10.67545
|
5
|
27.83077
|
27
|
11
|
12.64859
|
6
|
37.24490
|
36
|
28
|
14.02437
|
7
|
62.72287
|
55
|
39
|
26.90579
|
8
|
106.54754
|
101
|
93
|
35.61155
|
9
|
|
|
|
|
10
|
|
|
|
|
11
|
|
|
|
|
Data for exponents of 3
edit
Abundancy
|
Mean
|
Median
|
Mode
|
Standard deviation
|
2
|
0.01961
|
0
|
0
|
0.13865
|
3
|
0.66667
|
1
|
1
|
0.47140
|
4
|
4.66667
|
4
|
2, 4
|
2.77889
|
5
|
8.89231
|
8
|
5, 7
|
4.46223
|
6
|
9.67347
|
9
|
7, 8
|
4.63345
|
7
|
19.47674
|
19
|
20
|
5.87907
|
8
|
34.81514
|
34
|
33
|
8.88023
|
9
|
57.21211
|
57
|
58
|
10.84608
|
10
|
93.55906
|
93
|
96
|
13.032742
|
11
|
142.5
|
142.5
|
—
|
2.5
|
Data for exponents of 5
edit
Abundancy
|
Mean
|
Median
|
Mode
|
Standard deviation
|
2
|
0
|
0
|
—
|
0
|
3
|
0.5
|
0.5
|
—
|
0.5
|
4
|
0.47222
|
0
|
0
|
0.64490
|
5
|
1.35385
|
1
|
1
|
1.47211
|
6
|
4.03265
|
3
|
3
|
2.35063
|
7
|
7.81589
|
7
|
7
|
3.36463
|
8
|
14.51849
|
14
|
11
|
4.99204
|
9
|
28.61830
|
28
|
27
|
6.60122
|
10
|
44.00585
|
44
|
42
|
7.70645
|
11
|
69.5
|
69.5
|
—
|
3.5
|
Data for exponents of 7
edit
Abundancy
|
Mean
|
Median
|
Mode
|
Standard deviation
|
2
|
0.01961
|
0
|
0
|
0.13865
|
3
|
0.5
|
0.5
|
—
|
0.5
|
4
|
0.97222
|
1
|
1
|
0.68662
|
5
|
2.47692
|
2
|
2
|
1.99312
|
6
|
3.92245
|
3
|
3
|
2.16797
|
7
|
6.19961
|
6
|
7
|
2.60234
|
8
|
12.41373
|
12
|
10
|
3.83364
|
9
|
21.51848
|
21
|
19
|
5.37753
|
10
|
32.08421
|
32
|
32
|
6.43382
|
11
|
49
|
49
|
—
|
0
|
Where I get this data from
edit