1. If statistics are arranged so as to show the number of times, or frequency with which, an event happens in a particular way, then the arrangement is a frequency distribution. Although some of our results will be of wider applicability, we shall generally confine our attention to these distributions.

It is necessary to have a name for the formula used to describe such distributions, and the term ‘frequency-curve’ has been adopted for the purpose.

2. Some distributions give the number of cases falling in a certain group of values of the independent variable, while others (e.g. Example 5 of Table 1) give the number of cases for an exact value. In the former case the exact values of the independent variable to which the groups correspond must be considered; for instance, ‘exposed to risk at age x’ includes those from x−½ to x+½, but the number of deaths at duration n those from n to n+1. When statistics are represented graphically, effect should be given to these differences, and, to bring out the points a little more clearly, the diagrams on pages 6 and 7 have been prepared. Note that ‘curtate duration’ in Example 1 is naturally represented by a frequency polygon, as it takes only integer values, but if the data are regarded as giving actual duration they should be represented by a histogram, since generally ‘curtate duration n’ means ‘actual duration n to (n+1)’.