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UncleBucket

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A great many people seem to believe, for example, that if each temperature reading is accurate to +/- 0.5°, the reading should be rounded to the nearest integer. I don't have a problem with that, but when it comes to the calculation of the mean average, we have a difference of opinion. Many people seem to believe that if the list of values, for which the mean average is to be calculated, are all integers, then the mean average itself must also be an integer! This makes no sense at all to me.

Another person argues that because the list of values contains "measured approximations", it is not appropriate to express the mean average to 1 or more decimal places, and that any decimal digits must be truncated!

I welcome your views on these matters.

Just recently, I was browsing the Met Office website, and found a document which gives details of the accuracy of each instrument, and the margin of error when calculating the mean average. I will quote it:

The random error in a single thermometer reading is about 0.2°C (1 σ) [Folland et al., 2001]; the monthly average will be based on at least two readings a day throughout the month, giving 60 or more values contributing to the mean. So the error in the monthly average will be at most0.2/√60 = 0.03°Cand this will be uncorrelated with the value for any other station or the value for any other month.

I am not an expert in this field, so could someone please explain to me the validity of that formula and why it is correct, assuming it is. Clearly, the accuracy of the mean average appears to be greater than that of any of the individual values in the original list. Would this be because with a large sample of data, the errors within each instrument reading tend to cancel each other out?