In 1990, Mittendorf and colleagues pretty much established that a first pregnancy, on average, lasts longer than the 280 days from LMP that we use to calculate due dates.
http://www.ncbi.nlm.nih.gov/pubmed/2342739
Their research showed pregnancy, on average, to last 41 weeks and 1 day for primiparous women and 40 weeks and 3 days for multiparous women. They concluded that "one should count back 3 months from the first day of the last menses, then add 15 days for primiparas or 10 days for multiparas, instead of using the common algorithm for Naegele's rule" [Naegele's rule being count back three months and add 7 days]. Mittendorf et al.'s statistics did come from what they describe as "private-care white mothers" but, in the intervening quarter century, these findings haven't even been adopted for that demographic, with the inevitable impact on anxiety levels and intervention rates.
Roll on 23 years to 2013 and more of the same. http://humrep.oxfordjournals.org/content/28/10/2848
Not only is the average length of pregnancy 40 weeks and 2 days from LMP, according to this later research, but it also has a large natural variation, of 37 days. The sample was a lot smaller but again brings the honesty of giving women an Expected Date of Birth (EDB) instead of an Expected Period of Birth (EPB) into question. UM, like many midwives and doulas, has for many years preferred to talk about a rough estimate (taking into account Mittendorf and Co.'s paper) of, for example,"around the first week of May" or "the second half of June" or "the middle of November". But even this approach falters in face of the assertive and "scientific" certainty of an Expected Date of Delivery (EDD) (sic) given at a scan or medical appointment.
Let's all stop talking about EDDs ("women give birth, pizzas are delivered"), and EDBs and replace these with EPBs.
Of course this all begs the question of when is someone "overdue"? But the answer is clearly "not as soon as we think".