RELATION BETWEEN RENTS AND INCOMES 



103 



APPENDIX 



Mathematics of the Logarithmic Skew Curve 



Frequency curves may be symmetrical or skew. The particular 

 symmetrical distribution known as the normal curve of error is typical 

 of distributions of observational errors and in general of all phenomena 

 obeying the laws of chance. It is approximated by a number of other 

 distributions which have not obviously originated in the same way, 

 which implies that "the variable is the sum of a large number of 

 elements each of which can take the values and 1, these values 

 occurring independently and with equal frequency." Skew distri- 

 butions may take a variety of forms but the type shown in the dia- 

 gram is closely approached by a large number of rent distributions. 

 The essential characteristic of this curve, which may be called the 

 logarithmic skew curve, is that logarithms of the values of the variable 

 are distributed according to the normal curve of error. This skew 

 curve is of course not the only one which might be selected to repre- 

 sent rent data, but it presents the fewest mathematical difficulties 

 and gives a sufficiently close approximation for all practical purposes. 



-so -40 -30 -20 -10 O 10 20 30 



NORMAL CURVE OF ERROR 



20 30 40 50 60 '0 80 



LOGARITHMIC SKEW CURVE 



Fig. 8 



The normal curve of error has the equation 



1 _-£i 



y 



(tV2t 



(1) 



where e is 2.7183, the base of natural logarithms and a is a measure 

 of dispersion, known as the standard deviation. An ordinate of 

 the curve is called the frequency, and expresses the fraction of the 

 whole number of items which occurs per unit interval of the variable x. 



