摘要:

SummaryThe genesis of frequency distributionsThe next set of six short papers reproduces the contents of a series of six talks given at the annual meeting of the ‘Vereniging voor Statistiek’ (Statistical Society) having ‘frequency distributions’ for their subject.In this first and introductory paper the various ways in wich we may conceive a frequency distributions to be generated aye briefly indicated, and the useful conclusions with regard to the underlying sources of variation that may often be drawn from the shape of an observed frequency distribution are poin

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00418.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY

摘要:

SummaryAn demonstration of the Central Limit Theorem.For the dimension y of a screw‐plug cartridge fuse (fig. 1) the relationy = ‐a + b‐ c + d + eholds good, a, b, c, d, and e being certain dimensions of the component parts. Batches of components were sorted into two sub‐lots, each sub‐lot having a distribution truncated on one side (fig. 3). From one set of sub‐lots 300 sets of components were selected with the aid of random sampling numbers; these were assembled and the resultant dimension y of the assemblage observed. Despite the non‐normality of the distributions of the components the distribution of y is shown to be essentially normal:1by computing β1;2by plotting the cumulative distribution on arithmetic probability paper (fig. 4); and3by calculation o

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00419.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY

摘要:

SummaryFrequency distributions and mixing problems.If in packages of a powdered mixture a minimum quantity of some essential and expensive component has to be guaranteed, the degree of homogeneity of the mixture becomes an important industrial probIem. The greater the dispersion, the greater will be the overweight required in order to satisfy the prescribed minimum conditions. The problems which may arise under such conditions and the value of a study of the mixing process and its efficiency are briefly discussed. In essence they amount to a study of frequency distributions describing the properties of the mixture.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00420.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY

摘要:

SummaryTwo frequency distributions concerning the consumption of food.By interviewing, the caloric amount of food consumed by 294 different persons during a single day was determined and compared with the amount estimated from weight, length, age and sex according to standard practices. The quantityR = 100 log Calories observed/Calories estimatedhas a distribution shown in fig. 1. The variance is fairly large.In another experiment the caloric food consumption was determined for 22 different persons each day during a fortnight and the quantities.x' = 100 log Observed caloric consumption per day/Average caloric consumption per daywere computed and plotted in a histogram (fig. 2). The varaiance of x' is found to be considerably less (± 30) than the variance of R (122) from which it is concluded that errors inherent in the surveying technique were probably not the major cause of the high variance of R

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00421.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY

摘要:

SummarySome aspects of the spread observed in time studies.In the introduction the importance of time studies in mass production is mentioned. Next figures 1, 2 and 3 give some examples of the frequency distributions observed for the time intervals required for cyclical factory operations. It is pointed out that for comparing different jobs the specific deviation, s/√t, is often more useful than the standard deviation, s, or the average time t̄. If greater detail is required a study of the historic sequency may be of advantage; this sometimes reveals marked periodicity in speed (fig. 5). If one cyclical operation is split up in a number of phases, the variance of the whole is often larger than the sum of the variances of th; components, wich demonstrates the existence of correlations. Sometimes the distribution of 1/t or of 1/t2is found to be slcser to normal than that oft. In ajinal section the main causes of variation are briefly survey

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00422.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00423.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY

摘要:

SummaryThe use and the application of probability paper.The technique of plotting a frequency distribution as a cumulative distribution on probability paper, and of determining the average and the standard deviation in a simple way from such a plot, is described. It is emphasized that when we use this technique the choice of the size of the classes is relatively of little importance. Besides, the plot on probability paper renders it possible to evaluate in simplefashion the influence of changes in the mean or in the standard deviation on the percentage of observations falling above or below a given limit. The paper is concluded by a discussion of some examples in which the plot canaot be approximated by a straight line, and of the way in wich diflerent types of deviations may be explained.

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00424.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY

摘要:

SummaryThe utility of probability paper in studying the statistics of biological variations.This paper mainly deals with various applications and theorems concerning arithmetic probability paper.It is pointed out that the so‐called ‘normal function’ introduced by Kapteyn and Van Uven [1,2] is the same function as that which would be obtained by plotting the corresponding distribution on arithmetic probability paper. For a normal distribution the ‘normal function’ is a straight line, for a logarithmiconormal distribution it is a logarithmic curve.Galton's well‐known apparatus for demonstrating the genesis of a normal distribution (fig. 5) was modijied by Kapteyn (fig. 6) so as to produce a skew distribution. The latter apparatus can be transformed into the former by a process of stretching and compressing in a horizontal direction, and this transformation is again described by the ‘normal function’ of the non‐normal distribution shown in fig. 6.If the dividing blocks in these apparatus are conceived infinitesimally small and all of equal height, the path of those grains of small shot which always fall towards the right, or always towards the left, is again the ‘normal function’, or its image with respect to a horizontal line.Further some applications of probability paper in correlation studies and for the representation of certain laws of growth are discussed.In ‘Appendix I’ a method for χ2‐testing the reliability of a normal distribution fitted by means of probability paper is described, white in ‘Appendix II’ a mathematical proof is given of a number of theorems that were mer

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00425.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY

摘要:

SummaryThe adjustment of polynomials to a series of equidistant data.If a quantity Uxhas been observed for a set of equidistant values of x, and if we wish to adjust a polynomialto these data by the method of least squares, the coefficients kpcan be computed in the formwhere the Ep(x) are functions of x and p, the values of which may be taken from a table.Tables for this purpose for 1 ≦ N ≦ 6 and for series of observations up to 50 were computed and edited by the Weather Bureau in Pretoria. In this paper formulae for the computation of the functions Ep(x) are deduced from the analogous development in orthogonal plynomials. In a final section the method is illustrated by a particular example, namely the representation of average air pressure as a function of geographical latit

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00426.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY

ISSN:0039-0402    

DOI:10.1111/j.1467-9574.1950.tb00427.x

出版商:Blackwell Publishing Ltd    

年代:1950

数据来源: WILEY