Descriptive measure is that kind of measure that deals with the quantitative data in a mass which exhibits certain general characteristics. The descriptive measure is of different types for different characteristics of data. This document will discuss different descriptive measures for different types of data.
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There is a tendency for data to cause variation about the descriptive measure of central tendency. This descriptive measure of deviation is also called the descriptive measure of variation or dispersion.
The descriptive measure of deviation is a descriptive measure of the extent to which an individual item may vary. This descriptive measure of deviation of the data should satisfy certain properties which have been laid down by Prof. Yule. These properties are as follows:
The descriptive measure of deviation should be rigidly defined. This descriptive measure should be flexible in calculation and should be easy to understand. This descriptive measure should be based on all the observations. This descriptive measure should be open to further mathematical treatment. This descriptive measure should not be affected by the fluctuations of the sampling.
The descriptive measure of dispersion has been classified into two broad categories.
The descriptive measure of dispersion involves expressing the spread of observations in terms of distance. Such categories of descriptive measure of deviations include range and inters quartile range (or quartile deviation).
The descriptive measure of deviation called range is defined as the difference between the two extreme observations of the distribution. Suppose A and B are the greatest and the smallest observations respectively. In this case, the descriptive measure of deviation (i.e. range) is Range= A-B.
The descriptive measure of deviation called inter quartile range or quartile deviation is also called semi inter quartile range. This descriptive measure is defined mathematically as: Q= (Q3 – Q1)/ 2, where Q3 is the third quartiles and Q1 is the first quartiles. This descriptive measure is definitely a better measure than the previous descriptive measure, as this descriptive measure makes use of 50% of the data. However, this descriptive measure ignores the other 50 % of the data, therefore, this descriptive measure cannot be regarded as a reliable descriptive measure.
The descriptive measure expresses the spread of observations in terms of the average of deviations of the observations from some central value. Such categories of descriptive measure of deviation include mean deviation and standard deviation.
The mean deviation is a descriptive measure of deviation based on all the observations and is a much better type of descriptive measure then other descriptive measure of deviations. However, since in this type of descriptive measure of deviation the sign of the deviation has been ignored, this descriptive measure becomes useless for further mathematical treatment.
The standard deviation is a descriptive measure of deviation that is generally denoted by the Greek letter (σ). This type of descriptive measure is defined as the positive square root of the arithmetic mean of the squares of the deviation of the given values from their arithmetic mean. In this type of descriptive measure, the deviation is being squared. Thus, this descriptive measure overcomes the drawback of the descriptive measure of the mean deviation.
This is the only descriptive measure of deviation which satisfies almost all the ideal properties of the descriptive measure of deviation laid down by Prof. Yule, except for the general nature of extracting the square root which is generally not readily comprehensible for a non-mathematical person. It should be observed that this type of descriptive measure gives greater weight age to the extreme values and is not as popular in terms of being used by economists or businessmen.
