User:Ar Colorado/My useful information/Data for exponents of primes in multiply perfect numbers
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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
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
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
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
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 |