The standard deviation
Following are the data for the number of fire stations observed in 20 dif-
2 3 4 5 6 7 8 9 10
2 1 7 3 6 0 2
Plot a frequency distribution of the corresponding random variable.
Plot a cumulative frequency distribution function.
Find the average number of fire stations, as observed in the sample.
Find the sample variance.
Show that the average of the deviations from the sample mean
is always equal to zero.
Factor out the expression.) Justify this on
Show that the standard deviation is not equal to the average deviation from
Use the fact that";
ANG, A. H., AND W. TANG.
Probability Concepts in Engineering, Planning and
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.
A Systems View of Planning.
Elmsford, N.Y.: Pergamon Press,
An Introduction to Probability Theory and Its Applications.
Sons, Inc., 1969.
McLOUGHLIN, J. B.
Urban and RegionalPlanning.
. A Systems Approach.
Praeger Publishers, Inc., 1969.
Introduction to Linear Algebra for Social Scientists.
Unwin Ltd., 1968.
O'BRIEN, R. J., AND G. G. GAREIG.
Mathematics for Economists and Social Scien-
New York: Macmillan Publishing Co., Inc., 1971.
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
The study of the characteristics of a population and of their evolution
through time and space constitutes the field of
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