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

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

Where I get this data from

• List of multiply perfect numbers from Achim Flammenkamp