: Oz:
: >: You omit 'unbiassed' and that's only true to the limit of the accuracies
: >: of the devices and their resolution. Taking a million measurements with
: >: an inaccurate thermometer does not give you results with accuracies into
: >: the millidegrees.
: >
: >No.  That is not true.

: Yes it is.

: >For example, assume that you have an eight
: >bit digital readout.
: >If you average four readings that is equivalent
: >to a ten bit device.

: Assume that it is 100% accurate to -+ last digit.

  Why would anyone assume this?  Looks to me like you are trying to
assume what you wish to prove.

: >For analog measurements, it is a bit more complicated, but if the
: >deviations in reading are normally distributed then your precision
: >in determining the mean will improve roughly in proportion to
: >the square root of the number of measurements that you make.

: Only if the thermometer is 100% accurate.

  No.  If the thermometer was 100% accurate then the first measurement
would be perfect, as would all other measurements, thus the error would
be zero, and the median would never change or grow more precisely defined.

: If it comes from a batch NAMAS
: tested to be within 1C and actually reads 99.6C when the temperature is
: in fact 100C then your method will give 99.6C (if you are really lucky)
: with extreme apparent accuracy but none the less will in fact be 0.4C
: out. It will always be 0.4C out.

  If a thermometer is improperly calibrated, yes it will read
improperly.  But even here your complaint fails because calibration
errors can also be expected to be normally distributed about the correct
value.  As a result the bias in one thermometer will be cancelled by the
bias in another.

  Do you have evidence of systematic bias in thermometers?  Or are you
simply talking out your ass?

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