The study of turbulence in geophysical flows benefits from the growing amount of data available via modern sensor technologies. It is now possible to obtain detailed statistical characterisation of turbulence from field observations. By ``statistical,'' we mean the description of a turbulent flow by precisely characterising the probability density function of quantities as the fluctuations of temperature or velocity, the increments of temperature in time and space, etc. This approach, common in laboratory and numerical studies, is only now becoming feasible when using field observations, since the size of datasets now enables converged estimates of high-order statistical moments (i.e.~provide sufficient coverage of large deviations from the mean). Here, we provide an example of the value of such an exercise, with an application to deep ocean, wall bounded, stratified turbulence. Deep ocean data was collected using a moored array of 144 thermistors, 100m tall, deployed above the slopes of a seamount in the North Eastern Atlantic Ocean from April to August 2013. The thermistors, built in-house at the Royal Netherlands Institute for Sea Research, provide a precision better than 1mK, very low noise levels, and measure temperature every second, synchronised throughout the moored array. The thermistor array ends 5m above the bottom, and no bottom mixed layer is visible in the data, indicating that restratification is constantly occurring and that a mixed layer is either absent or very thin. Intense turbulence is observed, and a strong dependence of turbulence parameters on the phase of the semidiurnal tidal wave (the dominant frequency in the power spectrum) is also evident. We compute the statistical moments (generalised structure functions) of order up to 10 of the distributions of temperature increments. Strong intermittency and marked deviations from Gaussian behaviour are observed. We argue that these can be linked to different turbulence generation mechanisms (shear, convection) which dominate at different depths and during different tidal phases. High-order moments also show that the turbulence scaling behaviour breaks at a well-defined scale (of the order of the buoyancy length scale U/N), which is however dependent on the flow state. At larger scales, wave motions are dominant. This complex scaling behaviour testifies the strong variability at this location, in terms of turbulence intensity and forcing mechanism. However, when long term averages are considered, this complex behaviour is associated with a surprisingly simple functional relation among vertical heat flux, vertical temperature gradient and distance from the seafloor. This can be described by a mixing length model derived from Balmforth (1998), which takes into account the vertical squeezing effect on turbulent eddies due to both stratification and distance from the seafloor. Overall, the results suggest that surprisingly simple behaviour can be extracted from highly turbulent fields if sufficient averaging is performed. This is encouraging in terms of applications, as e.g.~simple wall turbulence models may be effectively used in large scale ocean or climate models. However, the results do not explain how the simple average behaviour originates from the complex turbulence dynamics.