According to this definition the numerical facts (data) should possess the following characteristics to be treated as statistics.

(i) Aggregate of facts:

Single, isolated or unrelated figures are not statistics, because they are not comparable. These figures tell nothing about any problem. For example the age of a student or the price of a commodity is not statistics. Because they are just abstract numbers. But when we consider age of a group of students, or the prices of a basket of commodities it is statistics as they comparable. Statistics must be expressed as aggregate of facts relating to any particular enquiry. Thus ‘not a datum’ but the data represent statistics.

(ii) Affected by multiplicity of causes :


Numerical facts should be affected by a number of factors to become statistics.These may include both normal as well as exceptional factors. For example, the yield of rice depends on a number of factors like the rainfall, fertility of the soil, method of cultivation, quality of seeds used etc.Some of these factors are normal and some are exceptional. Hence the data relating to the yield of rice over a period of time become statistics. On the other hand if we write numericals l,2,3,4,5,6,7,8,9,and 10, they are not statistics. Because they are not affected by any factors.

(iii) Numerically expressed:

Statistics are quantitative phenomena. Mostly, statistical techniques deal with quantitative factors than with qualitative aspect. So statistics should be always numerically expressed. For example, ‘there are 30 districts in Orissa’, is a numerical statement. But the standard of living of the people of Orissa have improved over the years’ is not a numerical statement. Here the first statement is statistical where as the second is not. So the subjective statements relating to qualitative information like honesty, beauties etc. are not statistics. Only statements which can be expressed numerically are statistics.

(iv) Enumerated accurately:


In an enquiry statistics (data) should be collected with a reasonable standard of accuracy. This affects the findings of the enquiry. The degree of accuracy of statistics depends on the nature and purpose of the enquiry. Generally data are collected in two ways – by enumerating all the units of the population (complete enumeration method) or enumerating some units (sampling Method) and the result is generalized for the whole group. No doubt the first method involves more time and cost but provides more accurate information than the second. Depending on the nature of enquiry and the degree of accuracy desired only one of the above two methods is employed. But the collected statistics should be as far as possible accurate.

(v) Collected in a systematic manner :

Information (data) constitute the basis of any statistical enquiry. They should be collected in a scientific and systematic manner. For this, the purpose of the enquiry must be decided in advance. The purpose should be specific and well defined. The information should be collected by trained, skilled and unbiased investigators. Other wise irrelevant and unnecessary information may be collected and the very purpose of statistics is defeated.

(vi) Collected for a predetermined purpose :


Statistics relating to an enquiry are always collected with a predetermined purpose. So it is essential to define clearly the purpose or the objective of the enquiry before actually collecting data. This ensures the inclusion of all essential information and the exclusion of all irrelevant and confusing data. This will make the analysis specific and result oriented.

(vii) Placed in relation to each other :

Statistics should be comparable. They may be compared with respect to time of occurrence or place of collection. This requires the data should be homogeneous and are placed in relation to each other. Because heterogeneous data are not comparable.For example, data relating to production of rice and the number of students taking admission in a class are not statistics. Because they are not comparable. On the other hand, the food grain production of a state for the last ten years constitute statistics as they are comparable. So statistical data should express some phenomenon. In other words, “All statistics are numerical statements of facts but all numerical statements of facts are not statistics”.