OJf FUTURE DEALINGS IN RAW PRODUCE. 



431 



dard Deviation, or, as it is sometimes called, the Probable Error of a 

 series of quotations as compared with the mean of the whole series em- 

 ployed. It seemed possible, however, that some serious fluctuations 

 would escape notice in this measui-e, in cases where rapid but only 

 moderately violent movements, now upwards, now downwards, charac- 

 terised the market quotations. A few very large variations seemed 

 capable of outweighing numerous smaller but quite serious movements. 

 To avoid possibility of a misleading result, therefore, the mean actual 

 difference between each quotation and that immediately following it has 

 also been calculated, and forms a second measure of the degree of varia- 

 bility of the price. In these comparisons the movements of wheat prices 

 have been deemed suflicient. 



The available series of daily quotations did not extend over a 

 sufficiently long period to make their use for our purpose quite satisfac- 

 tory. To test in some degree how far less frequent quotations might be 

 used without greatly disturbing the index obtained, some calculations 

 were made of the Standard Deviation for certain daily quotations and 

 other weekly quotations. The results indicate that the relative intensity 

 of fluctuations may be fairly well measured by weekly prices. 



It may be added that the S.D. of a series of weekly prices coincided 

 with remarkable closeness to that of a monthly series derived from them 

 over a period of half a century. The percentage of standard deviation to 

 average price is not widely different in the two cases. We have, there- 

 fore, considered that the relative steadiness of prices may be sufficiently 

 indicated from the weekly prices afforded in the Gazette Average Price of 

 English Wheat. Has the English farmer been subject to a less or greater 

 degree of fluctuation in the price of his wheat since futures-markets have 

 dominated those prices ? 



In the diagram annexed (see Appendix, Plate IV.), and in the tables 

 which accompany it, the comparison over fifty years is shown. Calendar 

 years have been used because the use of a fixed date from which to reckon 

 the cereal year introduced the difficulty that it sometimes threw price- 

 movements of two harvests into one so-called cereal year. Were the 

 cerea,! year able to be taken, the fluctuation shown might be somewhat 

 reduced. The computation of the S.D. for these years, making each 

 year begin with September, has been made, and no great difference" would 

 be shown had those results been plotted on the diagram in place of 

 those for calendar years. The summary of the tables in the Appendix 

 is as follows : — 



Gazette Averaye of English Wheat. 



Period 



Average Price s. d. per quarter 

 Standard Deviation 

 Mean Weekly Movement 



The gradual narrowing of the range of variation is a noteworthy 

 feature of the table. The fact that, considered as a percentage of the 

 price, the variability has hardly laeen reduced, is equally noteworthy; but 

 It IS a disputable point whether the actual money amount of the 

 variability is nor, rather to be taken into account than the percentao-e 



