I feel obliged to post the following information from time to time:
According to the largest scientific study of penis size, the mean (average) erect length was 13.12 cm (5.17 inches) with a standard deviation of 1.66 cm (0.65 inches).
What does this mean? Assuming that the sample (= 692) is representative of the population generally and that the data are distributed ”normally” (i.e., a “bell-shaped curve”),
68% of the population would be within one standard deviation of the mean [i.e., 13.12 cm (5.17 in) +/- 1.66 cm (0.65 in)] or between 11.46 and 14.78 cm (4.51 to 5.82 inches);
95% of the population would be within two standard deviations of the mean or between 9.8 and 16.44 cm (3.86 to 6.47 inches); and
99.7% of the population would be within three standard deviations of the mean or between 8.14 and 18.1 cm (3.2 to 7.13 inches).
Another way to put this is that if you take an erect penis at random (try it, it’s fun), there is a 15.87% chance of it being longer than 14.78 cm (5.82 inches), a 2.28% chance of it being longer than 16.44 cm (6.47 inches), and a 0.13% chance of it being longer than 18.1 cm (7.13 inches).
An 8 inch (20.32 cm) erect penis is 4.38 standard deviations above the mean. The probability of this occurring by chance is one in 1,464,792.
An 11 inch penis is 8.93 standard deviations above the mean. There is essentially no chance of this occurring. As a reality check, consider that the length of an erect penis that was 8.93 standard deviations
below the mean would be a negative number.
The study notes that these conclusions may be affected by the relatively small number of erect penises that were measured. It is also possible that penis size is not distributed normally and may be skewed in one direction or another.
Further reading:
Am I normal? A systematic review and construction of nomograms for flaccid and erect penis length and circumference in up to 15 521 men. https://doi.org/10.1111/bju.13010
“Nomograms for flaccid pendulous [n = 10 704, mean (sd) 9.16 (1.57) cm] and stretched length [n = 14 160, mean (sd) 13.24 (1.89) cm], erect length [n = 692, mean (sd) 13.12 (1.66) cm], flaccid circumference [n = 9407, mean (sd) 9.31 (0.90) cm], and erect circumference [n = 381, mean (sd) 11.66 (1.10) cm] were constructed. Consistent and strongest significant correlation was between flaccid stretched or erect length and height, which ranged from r = 0.2 to 0.6. Limitations: relatively few erect measurements were conducted in a clinical setting and the greatest variability between studies was seen with flaccid stretched length.”