The Gaussian distribution is an acceptable model for scatter if the number of elements in the data set is large. In practice we require . In many experiments it is not possible to repeat a reading such a large number of times either because of cost considerations or because of the nature the experiment itself. If the confidence interval is written as

where depends on In general increases as decreases; for , the limit is reached, the value appropriate for Gaussian distribution. The main effect of having a small number of data points is that the mean is not stationary and changes with . If it is assumed that the scatter in the mean is Gaussian it can be shown that the standard deviation in the mean is , where is the standard deviation in . The distribution that takes into account the changes in the mean value as well is called Student's distribution. Values of as a function of the degree of freedom and the percentage confidence interval are also available in tabular form (Table A2, Figure 1.16). Once is determined, the scatter in data is specified as