Statistics: difference between measures of central tendency and measure of variation

A central tendency=y refers to a central value or a representative value of a statistical series. It is difficult for anyone to understand or remember a large group of raw data. One would like to know the critical value which represents all the items in a series. Such a value is called central tendency or average value. For example it is very difficult to understand the data concerning the income of millions of Indians. However it is said that in 2001 average income of people in India was 16,000 per annum, It will be easy for us to guess the economic condition of most of the Indians. It is this average value which is called central tendency of the series. It is called measures of location. Thus measures of central tendency refer to all those methods of statistical methods of statistical analysis by which averages of the statistical series are worked out. According to Croxton and Cowden “an average is a single value within the range of the data that is used to represent all of the values in the series. Since an average is somewhere within the range of data, it is sometimes called measures of central value. According to Clark an average is a figure that represents the whole group.

Measures of variation:

According to brooks and dick dispersion or spread is the degree of the scatter or variation of the variable about the central value. According to Simpson and Kafka the measurement of the scatter ness of the mass of the figure in a series about an average is called measure of variation or dispersion. Measures of variations are needed for 4 basic purposes:
1. To determine the reliability of an average.
2. To serve as a basis for the control of variability.
3. To compare 2 or more series with regard to their variability.
4. To facilitate the use of other statistical measures.

Essentials of good average:

Since an average is a single value representing a group of values, it is desired that such a value satisfies the following properties:

1. Easy to understand: Since statistical methods are designed to simplify complexity, it is desirable than an average should be such that can be readily understood otherwise its use is bound to be very limited.
2. Simple to compute: An average should not only be easy to understand but also simple to compute so that it can be used widely. However though ease to computation is desirable, it should not be sort at the expense of other advantages that is if in the interest of greater accuracy, use of a more difficult average is desirable, one should prefer that.
3. Based on all the items: The average should depend upon each item of the series so that if any of the item is dropped the average itself is altered.
4. Not be unduly affected by extreme observations: although each and every item should influence the value of the average, none of the items should influence it unduly. If one or two very small or very large items unduly affect the average, that is either increase or decrease its value the average cannot be really typical if the entire series. In other words extreme may distort the average and reduce its usefulness.
5. Rigidly defined: An average should be properly defined so that it has one and only one interpretation. It should preferably be defined by algebraic formula so that if different people compute the average from the same figure they all get the same answer. The average should not depend upon the personal prejudice and bias of the investigator otherwise the results can be misleading.