: What is the dispersion of woman's ovulation day around the mean value which is 14th day? Everywhere there's information that ovulation happens at around 14th day of the cycle. But what is the mathematical meaning for the

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Dispersion is roughly 12 days
This study found that only 10% of those with a regular cycle of 28 days had ovulation in the 14th day, dispersion was from day 10 up to day 22. In this study, only 69 out of 696 cycles were regular.

Ovulation occurred as early as the eighth day and as late as the 60th day of the menstrual cycle. ?Figure1 shows the distribution of fertile days, generated by the smoothed distribution of ovulation days. Overall, an estimated 2% of women were in their fertile window by the fourth day of their cycle and 17% by the seventh day (based on 213 women). This percentage peaked on days 12 and 13, when 54% of women were in their fertile window. If ovulation was delayed, women reached their fertile days much later. Among women who reached the fifth week of their cycle, 4-6% were in their fertile window.
Current clinical guidelines about a woman's potentially fertile days have been based on two assumptions—that ovulation occurs 14 days before the next menses and that women are fertile for several days before and after ovulation. It follows that in the usual menstrual cycle lasting 28 days, the fertile days would fall between days 10 and 17.15 The assumptions are, however, outdated. Firstly, only a small percentage of women ovulate exactly 14 days before the onset of menses. This is true even for women whose cycles are usually 28 days long. Among the 69 cycles for 28 days in our study, ovulation occurred 14 days before the next menses in only 10%. Time from ovulation to next menses ranged from 7 to 19 days (days 10 to 22 of the menstrual cycle). Thus, the fertile window can occur much earlier or later in the cycle than clinical guidelines suggest. On average, at least 10% of women with regular cycles were in their fertile window on any given day of their cycle between days 6 and 21. The timing of the fertile window is even less predictable for women with less regular cycles, which includes adolescents and women in their perimenopause.

The timing of the “fertile window” in the menstrual cycle: day specific estimates from a prospective study BMJ. 2000 Nov 18; 321(7271): 1259–1262. PMCID: PMC27529 Allen J Wilcox, branch chief, David Dunson, investigator,and Donna Day Baird, senior investigator

This website by Dr. med. Elisabeth Raith-Paula provides the following graphic, which seems to be inline with the above cited study.

Image Taken From: Raith E., Frank P., Freundl G. (1994) Wie korrelieren die Zeichen und Symptome der periodischen Fruchtbarkeit zur Ovulation und untereinander?. In: Natürliche Familienplanung heute. Springer, Berlin, Heidelberg; doi.org/10.1007/978-3-662-22209-6_7