The chief characteristics of statistics can be analysed as under:
(i) It consists of aggregate of facts. In the plural sense, statistics refers to data relating to any field of enquiry. But the data to be called statistics proper, must consist of aggregates of certain facts. This means that a single and isolated fact, or figure like 75 ‘mark’ secured in a particular subject by a particular student, or death of a particular person on a particular day will not amount to statistics. In order that certain data may amount to statistics, it must be in the form of a set or aggregate of certain facts viz, 50, 25, 75 etc. marks secured by a certain class of students in certain test or sales of a firm effected over different times etc.
(ii) It is liable to be affected to a marked extent by multiplicity of causes. The data to be called statistics must not be of static, but of variable nature. This means that the data should be liable to considerable changes in their value at different times, places or situations. Further, the change in the values of the data should be the result of interaction of a number of factors and it should not be ordinarily traceable to any single cause, or factor as it happens in case of physical science, or experimental methods. For example, in case of chemistry, the result of water is traced to the mixture of two volumes of hydrozen and one volume of oxygen. But in case of social science like education, the result of a particular college may be on account of the inter-action of several factors viz., standard of students, standard of teaching, standard of valuation, standard of invigilation and standard of questions etc., the effects of which can not be studied separately. From this characteristic, it follows that statistics covers both physical and social sciences.
(iii) It should be numerically expressed. Another characteristic of statistics is that the data should be numerically expressed in order that the data or fact to be called statistics must be capable of being expressed in the form of some quantities viz., marks of 50,60,70,80, or sales of $20,000, $15,000 $75,000 etc. From this, it follows that qualitative facts viz. honesty, bigness, $75,000 etc. From this, it follows that qualitative facts viz. honesty, bigness, greatness etc will not amount to statistics unless they are converted into some quantitative equivalents.
(iv) It should be capable of being either enumerated or estimated. Another characteristic of statistics is that the data should be capable of being either enumerated i.e. exactly counted, or the number of data is not very wide or large, exact counting or measurement of data will be quite possible, and in that case there will be no room for difference or errors. But if the field of enquiry or the number of data is very wide, large or indefinite, the enumeration of the data will be quite impossible, and in that case the data are to be estimated. But in case estimation, some errors, or differences in counting and measurement are likely to take place which should be as minimum as possible. For this, estimation of the data should be made according to a reasonable standard of accuracy. The reasonable standard of accuracy will depend again, upon the nature and purpose of enquiry. For instance, if it is a case of salt, or iron, it will be all right if the weighing is approximated to a kilogram but, if it is a case of some valuable things like gold, or diamond, it will be highly erratic to approximate the weighing even to a gram, Thus, in case of estimation, reasonable accuracy must be maintained keeping in view the nature and of enquiry.
(V) It should be collected in a systematic manner. Another characteristic required of statistics is that the data should be collected in a systematic or methodical manner for that the data collected in a haphazard or unsystematic manner will lead to difficulties in the analysis and to erroneous conclusions. In the words of Prof. Sacrist, “Stary and loose bits of quantitative information, hearsay and unrelated materials gleaned here and there form indiscriminate sources having no common basis of selection, even when numerical cannot be termed as statistics cannot be termed as statistics.” Thus, a proper plan, or a schedule should be the data in order that they may result in statistics and conform to reasonable standard of accuracy.
(vi) It should be collected for a pre-determined purpose. Another characteristic required of data to be regarded as statistics is that they should be collected with a predetermined purpose or objective. This means that before starting with collection of the data, the purpose or objective of collection should be designed. Any data collected without a pre-determined purpose may not be appropriate and useful for a purpose decided later on the vehicles passing by him, it will not amount to statistics for that there is no purpose behind the collection of such data.
(vii) It should be capable of being placed in relation to each other. The last but not the least important characteristics of the data to be called statistics is that it should be capable of being placed in relation to each other. This means that the data should be of homogeneous character to allow for comparison between them. Heterogenous data like sale of $10,000, result of 60%, crime of 50 cases and mileage of 30 kms can never be placed in relation to each other and compared for analysis and interpretation which are the chief functions of the science of statistics.