RE: Margin of error
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For the global data, the 95% envelope is roughly +/-0.15C, but varies slightly each month/year based on data coverage. You can see exact values in our reports, for example the tables here: https://www.ncdc.noaa.gov/sotc/global/201611
For the US, a previous CONUS dataset had trend uncertainties estimated as +/-0.015C per decade (please see http://journals.ametsoc.org/doi/pdf/10.1175/2008BAMS2613.1 for details). Please note, however, that USHCN is no longer the basis for our estimates of US temperature, and uncertainty estimation is an ongoing area of focus at NCEI.
Thanks
Deke