We had learnt how to present a statistical data precisely and meaningfully. This is to enable the statistician to study the data well and draw inferences from the,‘data. But by presentation only, it cannot be possible. Hence after presenting the data, it should be condensed. Condensation of data is essential in statistical analysis because, a large number of figures not only confusing but difficult to analyse also. In order to reduce the complexity of data and to make them comparable, it is essential that various characteristics which are being compared are reduced to one figure each. If, for example, a comparison is made between the marks obtained by 45 students belonging to Batch-A of plus-1 and 48 students belonging to Batch-B of plus-1 of your school in the first term examination, it would be impossible to arrive at any conclusion, if the two series relating to these marks are directly compared. On the other hand, if each of these series is represented by one figure, comparison would be easier. It is, obvious that a figure which is used to represent a whole series should neither have the lowest value in the series nor the highest value, but a value somewhere between these two limits, possibly in the centre, where most of the items of the series gather. Such a figure is called the average or a measure of central tendency.
The average represents the whole series and as such, its value always lies between the highest and the lowest values and generally it is located in the centre or middle of the distribution. Thus, central tendency summarises the data in a single value in such a way that this single value can represent the entire data. A measure of central tendency is a single figure that is computed from a given series to give a central value about the entire series. Hence a measure of central tendency may be defined as a typical value around which the values of a distribution congregate.
- It should be easy to understand
- It should be simple to compute
- It should be based on all the items
- It should not be unduly affected by extreme items
- It should be rigidly defined
- It should be capable of further algebraic treatment
- It should have sampling stability
- ARITHMETIC MEAN
- Simple Mean
- Combined Mean
- Weighted Mean