Question

define statistics state any 6 features and limitations

Answer 1

The branch of mathematics that deals with the collection, organization, analysis, and interpretation of numerical data. Statistics is especially useful in drawing general conclusions about a set of data from a sample of the data.

1. Statistics are aggregate of facts

A single age of 20 or 30 years is not statistics, a series of ages are. Similarly, a single figure relating to production, sales, birth, death etc., would not be statistics although aggregates of such figures would bestatistics because of their comparability and relationship.

2. Statistics are affected to a marked extent by a multiplicity of causes

A number of causes affect statistics in a particular field of enquiry, e.g., in production statistics are affected by climate, soil, fertility, availability of raw materials and methods of quick transport.

3. Statistics are numerically expressed, enumrated or estimated

The subject of statistics is concerned essentially with facts expressed in numerical form—with theirquantitative details but not qualitative descriptions. Therefore, facts indicated by terms such as ‘good’, ‘poor’ are not statistics unless a numerical equivalent, is assigned to each expression. Also this may either beenumerated or estimated, where actual enumeration is either not possible or is very difficult.

4. Statistics are numerated or estimated according to reasonable standard of accuracy

Personal bias and prejudices of the enumeration should not enter into the counting or estimation of figures, otherwise conclusions from the figures would not be accurate. The figures should be counted or estimated according to reasonable standards of accuracy. Absolute accuracy is neither necessary nor sometimes possible in social sciences.

5. Statistics should be collected in a systematic manner for a predetermined purpose

The statistical methods to be applied on the purpose of enquiry since figures are always collected with some purpose. If there is no predetermined purpose, all the efforts in collecting the figures may prove to be wasteful.

6. Statistics should be capable of being placed in relation to each other

The collected figure should be comparable and well-connected in the same department of inquiry. Ages of husbands are to be compared only with the corresponding ages of wives, and not with, say, heights of trees.

Limitations of Statistics

The scope of the science of statistic is restricted by certain limitations :

1. The use of statistics is limited numerical studies: Statistical methods cannot be applied to study the nature of all type of phenomena. Statistics deal with only such phenomena as are capable of being quantitatively measured and numerically expressed. For, example, the health, poverty and intelligence of a group of individuals, cannot be quantitatively measured, and thus are not suitable subjects for statistical study.

2. Statistical methods deal with population or aggregate of individuals rather than with individuals. When we say that the average height of an Indian is 1 metre 80 centimetres, it shows the height not of an individual but as found by the study of all individuals.

3. Statistical relies on estimates and approximations : Statistical laws are not exact laws like mathematical or chemical laws. They are derived by taking a majority of cases and are not true for every individual.

4. Statistical results might lead to fallacious conclusions by deliberate manipulation of figures and unscientific handling. This is so because statistical results are represented by figures, which are liable to be manipulated. Also the data placed in the hands of an expert may lead to fallacious results. The figures may be stated without their context or may be applied to a fact other than the one to which they really relate. An interesting example is a survey made some years ago which reported that 33% of all the girl students at John Hopkins University had married University teachers. Whereas the University had only three girls student at that time and one of them married to a teacher.