How do airlines handle uncertainty in passenger weight for weight and balance calculations? When commercial airlines calculate the mass and distribution of passenger load, in the cases where they do not weigh the passengers directly, they use standard weight measures which have been approved by the appropriate aviation authority.

The standard weights can be broken down by passenger type (adult/child), by sex (male/female) and by other factors such as season or business/economy class. To obtain these figures a survey is carried out at an airport and appropriate measures are taken to ensure the sample is representative.

The result is a single value that represents the standard weight for a male/female/child/etc. Whilst the standard weight may have a minimal bias (i.e. a small deviation from the population mean), it does not represent the variance of the observed passenger weights. That is if the sample mean is 90kg with a std deviation of 10, the there is a ~15% chance that a passenger has a weight more than 100kg (assuming normal distribution, for the purpose of this example).

Given that airline operators have to be extremely careful and conservative with their weight management how do they account for this uncertainty in their calculations? Using the example above, if there were a flight with 100 passengers each >100kg, there would be an underestimation of mass by over 1 tonne (relatively small in comparison to total loaded aircraft mass, but still a large figure in itself).

Are accommodations for this variation incorporated into the standard passenger weight (say use mean + x std. dev.) or does this get included in the operational limits that the airline set for their max weight allowances in their various forms, for example reduced Max Zero Fuel Weight (MZFW) or Max Take Off Weight (MTOW)?

Edit: This is a slightly different question to a similar one about how a commercial aircraft has its mass determined. The focus here is more specific in looking at how the standard passenger weights are calculated and what are the assumptions around using that data.
They don't handle that uncertainty.

Safety is always the prominent factor in the aviation industry. That said, measurements need only to be "accurate enough" for the purpose of safety. Being off by small amount would not compromise safety.

Furthermore, the atmospheric condition is always different; it is so dynamic and cannot be precisely measured. As long as the measurement is accurate enough, the aircraft will fly.

Theoretically, you could argue that there's a chance:


calculated weight is already at MTOW
every passenger happens to weight way above average
they all bought a lot of souvenir at the airport shops
density altitude was extraordinary high
a 10 knots tailwind was present at takeoff


and the aircraft overrun the runway during its takeoff roll. However, such a chance is so small that we accept our current method as it is and expect the aircraft to tolerate that uncertainly within its designed safety factors.

Such believe was found to be wrong when a small aircraft crashed on takeoff in 2003. Regulations were then modified so that on a small enough aircraft, the actual weight of each passenger (plus luggage) must be used, rather than using a standard weight for estimation.