Practical statistical errors on a number basis

The mean, on a number basis, can be calculated from experimental data using the following equation  

If the true mean is not known, the experimental mean, determined using equation (1.8), must be used. In this case the denominator in equation (1.9) is replaced by ( - 1), which has a negligible effect when n is large. 

Assume that the sampling operation described in example 1 is carried out II -= 1000 times with the results presented in Table 1.4. Then, from equation 1.9, the standard deviation cr = 35.9, which is 2.87 times the theoretical value. If the true mean (4000) is not known the experimental mean, which equals 3985 by equation (1.8), must be used and the denominator in equation (1.9) is replaced by ( -1). The resulting standard deviation o = 32.4 is very similar to the previous value due to the large number of samples taken. 

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