SEA-FISHERIES LABORATORY. 145 



Tanuary to October, 1909, is 1*034. The similar average 

 for Rock Channel plaice for the same months is 0*966. 

 The former fish are therefore in better condition, since 

 the average value of Jc is greatest. 



Now these mean values are deduced from samples; 

 obviously the latter must be unreliable to some extent, 

 since we can never sample an assemblage of organisms 

 in the sea without error; and it is necessary to ascertain 

 the limits of error whenever a comparison of two or more 

 series of samples is made. The precision of the mean 

 depends on the extent to which the data averaged 

 " scatter " from the maximum point in the series, and is 

 deduced from the standard deviation. The arithmetic 

 mean (or average) in the case of the Barrow Channel 



series is 1*034, and the standard deviation <r, 



'ST 



'■^■^O'OSOS: Xv 2 being the sum of the "second 



N 



about the mean, and N=10, the number of 



V 



observations. The probable error of the mean is —p=* 

 and is 0*025. 



" Unless a result exceeds the expected by two or three 

 times the probable error, it is not safe to assume that the 

 particular case differs from the expected result.*' Now 

 the mean value of k in the Rock Channel statistics is 

 0*966, and differs from the mean of the Barrow Channel 

 statistics by 0068. The difference is therefore 2*6 times 

 the value of the probable error, and we are justified in 

 regarding it as significant, and indicative of a real 

 difference in the condition of the two fish populations 

 sampled. 



If a complete series of weight statistics for the plaice 

 of the Beaumaris — Red Wharf grounds were available, 

 we should probably find a corresponding significant differ- 



