STA301 Statistics and Probability GDB 1 Solution Spring 2013

What does dispersion indicates about the data ? Why is this of great importance ? Solution: Measures of dispersion are needed for four basic purposes: (i) To determine the reliability of an average. (ii) To serve as a basis for the control of the variability. (iii) To compare two or more

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series with regard to their variability. (iv) To facilitate the use of other statistical measures. A brief explanation of these points is given below: (i) Measures of variation point out as to how far an average is representative of the mass. When dispersion is small, the average is a typical value in the sense that is closely represents the individual value and it is reliable in the sense that it is a good estimate of the average in the corresponding universe. On the other hand, when dispersion is large the average is not so typical, and unless the sample is very large, the average may be quite unreliable. (ii) Another purpose of measuring dispersion is to determine nature and cause of variation in order to control the variation itself. In matter of health, variations in body temperature, pulse beat and blood pressure are the basic guides to guides to diagnosis. Prescribed treatment is designed to control their variation. In industrial production efficient operation requires control of quality variation, the cause of which are sought through inspection and quality control programmes. Thus measurement of dispersion is basic to the control of cause of variation. In engineering problems measures of dispersion are often especially important. In social sciences a special problem requiring the measurement of variability is the measurement of “inequality” of the distribution of income or wealth, etc. (iii) Measures of dispersion enable a comparison to be made of two or more series with regard to their variability. The study of variation may also be looked upon as a means of determining uniformity or consistency. A high degree of variation would mean little uniformity or consistency whereas a low degree of variation would mean great uniformity or consistency. (iv) Many powerful analytical tools in statistics such as correlation analysis, the testing of hypothesis, the analysis of fluctuations, techniques of production control, cost control, and so on are based on measures of variation of one kind or another.