Descriptive measure

Descriptive measure is basically a type of measure that deals with quantitative data in a mass that shows certain kinds of general characteristics. Descriptive measure is generally of different types for the different types of characteristics of data. This document will detail the different types of descriptive measure.

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A tendency that depicts the absorption around specific values, especially around the center, is called the descriptive measure of central tendency. This descriptive measure depicts the central tendency in data that should satisfy several properties. These properties were discussed by the famous statistician, Professor Yule.

The descriptive measure that shows the central tendency must be strictly defined. The descriptive measure that shows this tendency is generally flexible and simple to calculate and understand. The descriptive measure that exhibits such kinds of tendencies must be based on all the observations. The descriptive measure that has this kind of tendency must be adaptable for any kind of mathematical treatment. The descriptive measure that has such tendencies must not get affected by the extreme values in the observations.

The arithmetic mean is the descriptive measure that depicts the centering of the observations. The descriptive measure is defined as the overall sum of the observations in the data that are divided by the number of the observations in the data. This descriptive measure follows the main conditions of the properties that are explained by Professor Yule. The major limitation of the descriptive measure that shows central tendency is that such a descriptive measure cannot be obtained by inspection. This descriptive measure that shows the central tendency cannot be located graphically. This type of descriptive measure that depicts the central tendency cannot be calculated by the researcher if any particular observation is missing from the data. This descriptive measure, which shows the central tendency, is not applicable for that kind of data that shows qualitative characteristics.

The descriptive measure that shows the central tendency also has a descriptive measure called the weighted mean. This descriptive measure also works in a similar manner to arithmetic mean, except for the fact that this descriptive measure attaches weights to the items under consideration according to their importance in the life of the user. For example, if one wants to obtain the cost of living of a certain group of people, then the arithmetic mean descriptive measure will give importance to all the commodities, while the weighted mean descriptive measure gives more weight to certain commodities.

Median is another type of descriptive measure that depicts the central tendency. This descriptive measure is the only measure that is applicable when the researcher is dealing with qualitative data. This descriptive measure is defined as the value that conducts the partition of the data into two equal parts. The limitation of this kind of descriptive measure is that this measure is not adaptable to the algebraic treatment. Also, this kind of descriptive measure is not at all based on all the observations. If the observations are of even numbers, then this descriptive measure cannot be determined appropriately. This descriptive measure is used by the researcher to address the various issues, like the problem concerning wages, the distribution of wealth, etc.

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. Because there are different measures for the different types of data, this document will discuss these different descriptive measures.

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First, the descriptive measure of deviation or dispersion is a descriptive measure that measures 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, the descriptive measure should be easy to understand and it should also be flexible in calculation. This descriptive measure should also be based on every observation. Further, the descriptive measure should be open to any further mathematical treatment. And finally, the descriptive measure 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. The descriptive measure of skewness 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 of descriptive measure 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.