Descriptive Measure
Descriptive measure can be defined as the kind of measure dealing with the quantitative data in a mass that exhibits certain general characteristics. The descriptive measure has different types, all depending on the different characteristics of the data.
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First, the descriptive measure of deviation or dispersion is a measurement to the extent to which an individual item can vary. Professor Yule has laid out certain properties that the descriptive measure of deviation of the data should satisfy.
For one, the descriptive measure of deviation needs to be rigidly defined. Additionally,it should be easy to understand and it should also be flexible in calculation. This descriptive measure should also be based on every observation. Further, it should be open to any further mathematical treatment. And finally, it should not be affected by fluctuations in the sampling.
Whenever a researcher wants to make a comparison in the variability of the two series which differs widely in their averages, then the researcher calculates the coefficient of dispersion based on different types of descriptive measures of deviation or dispersion. There are four coefficients of dispersion based on different descriptive measures of dispersion or deviation: range, quartile deviation, mean deviation, and standard deviation.
The coefficient of variation is a hundred times the coefficient of dispersion that is based on the descriptive measure of dispersion which is standard deviation.
The data in a frequency distribution may fall into symmetrical or asymmetrical patterns and this measure of the direction and degree of asymmetry is called the descriptive measure of skewness. This refers to lack of symmetry. The researcher studies the descriptive measure of skewness in order to have knowledge about the shape and size of the curve through which the researcher can draw an inference about the given distribution.
A distribution is said to follow the descriptive measure of skewness if mean, mode, and median fall at different points. This type will also follow in the case when quartiles are not equidistant from the median and also in the case when the curve drawn from the given data is not symmetrical.
There are three descriptive measure of skewness.
The first type of descriptive measure of skewness is M- Md, where Md is the median of the distribution.
The second type of descriptive measure of skewness is M-M0, where M0 is the mode of the distribution.
The third type of descriptive measure of skewness is (Q3- Md)-( Md – Q1).
These are also types of absolute descriptive measures of skewness.
The researcher calculates the relative measure for the descriptive measure called the coefficients of skewness which are the pure numbers of independent units of the measurements.
Karl Pearson’s coefficient of skewness for the descriptive measure of skewness is the first type of coefficient of skewness that is based on mean, median and mode. This coefficient for the descriptive measure of skewness is positive if the value of the mean is more than the value of mode. Or, the median and the coefficient for the descriptive measure of skewness is negative if the value of mode or median is more than the mean.
Bowley’s coefficient of skewness for the descriptive measure of skewness is the second type of coefficient of skewness that is based on the quartiles. This type of coefficient of skewness for the descriptive measure of skewness is used in those cases where the mode is ill defined and the extreme values are present in the observation. It is also used in cases where the distribution has open end classes or unequal intervals.