Applied Models in Urban and Regional Analysis_Demographic Models

Applied Models in - r I I A pplied M odels i n U rban a nd R egional A nalysis I N ORBERT OPPENHEIM Polytechnic Institute o f New York

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r , I I I Applied Models in Urban and Regional Analysis NORBERT OPPENHEIM Polytechnic Institute of New York PRENTICE-HALL, INC., Englewood Cliffs, New Jersey 07632
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CH. I INTRODUCTION 30 Compute: (a) The mean J.L (b) The variance a Z (c) The standard deviation a 1.11 Following are the data for the number of fire stations observed in 20 dif- ferent localities: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 nl 13 10 2 1 7 3 6 0 2 8 3 6 5 2 3 0 5 12 (a) Plot a frequency distribution of the corresponding random variable. (b) Plot a cumulative frequency distribution function. (c) Find the average number of fire stations, as observed in the sample. (d) Find the sample variance. 1.12 Show that the average of the deviations from the sample mean lin ~ (XI - I X) is always equal to zero. (Hint: Factor out the expression.) Justify this on physical grounds. 1.13 Show that the standard deviation is not equal to the average deviation from the mean. (Hint: Use the fact that"; a Z + b 2 =F a + b.) REFERENCES ANG, A. H., AND W. TANG. Probability Concepts in Engineering, Planning and Design, Vol. 1. New York: John Wiley & Sons, Inc., 1975. BLALOCK, H. M. Theory Construction: From Verbal to Mathematical Formulations. Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1969. CHADWICK, G. A Systems View of Planning. Elmsford, N.Y.: Pergamon Press, Inc., 1971. FELLER, W. An Introduction to Probability Theory and Its Applications. New York: John Wiley & Sons, Inc., 1969. McLOUGHLIN, J. B. Urban and RegionalPlanning. . A Systems Approach. New York: Praeger Publishers, Inc., 1969. MILLS, G. Introduction to Linear Algebra for Social Scientists. London: George Allen & Unwin Ltd., 1968. O'BRIEN, R. J., AND G. G. GAREIG. Mathematics for Economists and Social Scien- tists. New York: Macmillan Publishing Co., Inc., 1971. 2====== Demographic Models 2.1 Introduction Planning and analysis in this book refer to planning for community develop- ment and analysis of public policy. Thus, these activities must be based on the knowledge of the makeup of the population to which these plans are directed. The size, age distribution, socioeconomic status, and ethnic dis- tribution of the population are essential factors in the preparation of a plan or the determination of policy alternatives. Of course, it is always possible to determine the existing values of these characteristics either by census or by survey research methods. However, plans and policy are by nature oriented toward the future. Thus, estimates of the composition of a given population at.a future date will be necessary. The purpose of this chapter is to introduce some of the basic methods of population projection. The study of the characteristics of a population and of their evolution through time and space constitutes the field of demography. This is a highly technical field, and a thorough exposition would require much more than one chapter. Thus, although one would not expect a planner or policy analyst to be an expert, he or she will need to understand the fundamental demographical methods.
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Applied Models in - r I I A pplied M odels i n U rban a nd R egional A nalysis I N ORBERT OPPENHEIM Polytechnic Institute o f New York

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