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The World of Statistics (1)
By Dr. Magdi Abadir, PhD
Article – 11: Measures of Dispersion (1)
1. The concept of dispersion
A factory produces large steel pipes of 48" diameter. Due to fluctuations in operating conditions, the actual diameters of pipes range from 47.5 to 48.5". A sample of 100 pipes chosen at random produced the distribution illustrated by the frequency polygon shown in Figure (1). Calculation of the average diameter results in about 48". It can be seen that the distribution is rather centered about that figure. Actually, 70% of the sample have their diameters ranging from 47.9 to 48.1". In such centered distribution, the mean value is actually representative of the whole distribution.On the other hand, consider the distribution shown in Figure (2) which also produces an average diameter of about 48". The diameters are much more scattered about the mean value. In such scattered distribution, the mean value is rather a numerical figure that does not typify the whole distribution.
2. Measures of dispersion
2.1 The rangeConsider the following distribution of scores in a class consisting of 10 students (With a maximum score of 10).
| 1 | 3 | 4 | 5 | 6 | 4 | 6 | 5 | 2 | 10 |
The minimum and maximum scores are 1 and 10 respectively. The range is the difference between these two scores = 9. That is,
Range = Xmax-Xmin
This means that the distribution spreads over 9 numbers. This figure is misleading since if the top student (of score 10) were discarded, the range would have been 6 – 1 = 5. The score (10) is said to be an outlier since it gives a false indication about the level of these students. This can also be proved by calculating the average score. If all entries were included, the average score = 4.6, while if the outlier is discarded, the mean score drops down to 4. This is the reason why; the range is seldom used as measure of dispersion as it is extremely sensitive to the presence of extreme values.
References:
(1) https://www.toppr.com/guides/business-mathematics-and-statistics/measures-of-central-tendency-and-dispersion/measure-of-dispersion/
| Dr. Magdi Fouad Abadir, Ph. D.: Dr. M. F. Abadir is currently a professor with the Chemical Engineering Department at the Faculty of Engineering, University of Cairo, Egypt. His major interests are in the fields of high temperature science and technology. During his career, he has supervised more than 110 MSc and PhD theses and published more than a hundred papers mostly in international peer review journals. He currently teaches courses in High Temperature Technology and Industrial Statistics. He is also a consultant for several industrial businesses. |
