3.4.2.1. Average Deviation 



The average deviation is defined mathematically as the sum of the absolute 

 values of each individual deviation divided by the total number of deviations ob- 

 served. The absolute value of course is the value vi^ithout regard to its sign. 



3.4.2.2. Standard Deviation 



The standard deviation is mathematically defined as the square root of the "sum 

 of the squares of each individual deviation divided by the number of deviations ob- 

 served". The mathematical significance of the standard deviation can be found in 

 most mathematical text books and will not be taken up here. It suffices to say that 

 the standard deviation is considered the most probable average for the deviation 

 where normal or Gaussian distribution of the readings is evident. 



3.4.3. Discrepancy 



Where it is desired to compare the simultaneous readings of two different in- 

 struments, as opposed to a series of measurements by a single instrument, the dif- 

 ference in reading between the two instruments can be called the discrepancy. This 

 is an arbitrary term which will be used here to avoid ambiguity. 



An average discrepancy will define the average of a group of discrepancies be- 

 tween two instruments measuring the same value. Its mathematical treatment is 

 similar to the average deviation. 



3.4.4. Variance 



When it is desired to describe the change over a period of time of an average 

 error or average deviation, it is convenient to call this change the variance. 



3.4.5. Variability 



In considering a series of measurements of conditions which do not change ap- 

 preciably with time, it is possible that conditions will vary slightly in the immediate 

 vicinity where the measurements are taken. The deviations in measurements will, 

 therefore, be a function not only of the instrument variations, but also of variations 

 in the conditions being examined. This latter variation is called variability and can 

 be described in terms of average or standard deviations,, where such deviations are a 

 true measure of the change of conditions. The term variability should not be con- 

 fused with the term variance used in the previous section. 



3.5. Other Terminology 



In an eflfort to clarify and perhaps to standardize the nomenclature used to 

 describe the errors of the Bathythermograph a glossary of pertinent terms is at- 

 tached as an Appendix to this report. It is hoped that this glossary will not only 

 serve to clarify the terminology used in this report, but will also act as a basis 

 for a more extensive and amended glossary in the field of Oceanography and Bath- 

 ythermography. 



3.6. Overall error as a function of individual errors 



Where the overall error of an instrument is a result of the contribution of 

 many individual types of errors as, for instance, reading error, correction errors, 

 instrument precision and dependent error, the overall error cannot be less than 

 the maximum of any one individual contribution, nor can it be greater than the 



