RELATION BETWEEN RENTS AND INCOMES 101 



$2000-5000, and comparatively few incomes over $20,000. New 

 Jersey occupies an intermediate position. Alabama, more or less 

 typical of Southern states, shows a much smaller number of returns 

 in proportion to population than any of these states, and a distribu- 

 tion nearly, but not quite, as closely grouped as Iowa. The fact 

 that a particular shape of curve is typical of a given state, and that 

 the curves are different for different states, corresponds to similar 

 characteristics of rent curves for cities. British income statistics 

 show about the same degree of dispersion as do returns for the United 

 States as a whole. 



Distributions of the logarithmic skew type may be found in other 

 fields than those of incomes and house rents. The theory has been 

 advanced by some statisticians that while the normal curve of error 

 is characteristic of observational errors, errors of estimate agree with 

 that law if logarithms rather than actual estimates be considered. 

 Price fluctuations, corporation earnings, and the profits of farmers 

 are distributed in a similar manner. The lengths of life of telephone 

 contracts agree quite closely with this type of distribution, if we 

 allow for the fact that very long lives are relatively few in number 

 because they started when the telephone business was comparatively 

 small. A peculiarity of rent distribution is that if we choose only 

 families having telephone service, or families having any one class 

 of service, we obtain a logarithmic skew distribution about as closely 

 as though we plotted all families in a city. 



Application to Survey Data. The charting method described above 

 was applied to rent data for 57 cities, both for composites of private 

 residences, flats and apartments and for private residences alone. 

 Table VIII gives the median rents and values of the rent dispersion 

 index Q^ for the composite data. Results for private residences 

 differ in most cases only very slightly from the results given; there 

 is no dominant tendency for the spread of private residence rents to 

 be greater or less than that of all rents in a city, but the median rent 

 in private residences is usually somewhat greater than that for the 

 composite. 



An effort was made to determine the significance of the various 

 values of the index Q, but the results are chiefly negative. There 

 is some tendency for the smaller cities to have a wide spread of rent 

 values; i.e., a high value for Q, but there is considerable scattering 

 of the data. This tendency is most apparent in the South, where the 

 smaller cities have extremely high values for Q. The relationship 

 between the index Q and the per cent of families with telephone 

 • See Appendix for a quantitative definition of Q. 



