There has been a lot of argument about GHCN adjustments. Fiddly stuff like whether a certain step introduced in Reykjavik in 1963 was justified. None of this has any significance for a global average. Steve Mosher of BEST is constantly reminding that there is actually a huge amount of data in the average, and there is no point in focussing on the very local scale.
That is a point I was emphasising in this post on homogenisation. The average is little affected by unbiased noise (cancellation), but sensitive to bias. So it makes sense to identify and eliminate bias, even if it increases noise. Homogenise.
There is another common naysayer claim, that averages are not more accurate than the original readings, as in this WUWT thread. I don't know what they think drug companies etc go to great expense to get a large set of responses to average.
Anyway, in this post I'll give a dramatic demonstration of the noise suppression of averaging. I'll take the usual post-1900 monthly GHCN and ERSST data and let TempLS calculate an annual average. Then I'll add Gaussian noise to every single monthly average. Big noise - amplitude (sd) 1 °C. That's a world in which thermometers can barely be read to the nearest degree. In fact much worse, since monthly averaging already reduces noise. Then I'll recompute and show the differences in various ways. I'll do 10 instances.
As you'll guess, the difference is small. The standard deviation of fluctuations about the unperturbed is about 0.006 °C. The effect on trend is even smaller. The unperturbed trend 1900-2014 is 0.7073 °C/Century and the range is about 0.705 to 0.710.
I should emphasise that this perturbation operates on what might be taken to be measurement error, and does not emulate that quoted by NASA, NOAA etc, which is dominated by spatial sampling error. It also assumes white (ie independent) noise; dependence will increase the effect. But from a very low base.
So here is the plot of time series of a single perturbation (red) against unperturbed. The change is barely visible. 1°C unbiased noise added to the individual monthly averages makes scarcely any difference.
So I'll plot the differences over time. This time I'll show the 10 instances - the signal is effectively random. The horizontal lines show the mean and 1 sd range. Note the y-axis scale.
Finally I'll show a plot of 1900-2014 trends. As mentioned, the unperturbed is 0.7073 and the range about +-0.0025; about 0.4%.