Mean 359 



chology, education, economics, and other branches of knowledge. 

 In one specific problem, each group of measurements represents 

 a group of plants. In general, such a group would be known as 

 a population. Thus each family would comprise a different popu- 

 lation. If we consider a population such as the Fi generation 

 from a cross between a plant of Nicotiana Langsdorffii and one 

 of N. alata, how many plants would be included in such a popu- 

 lation? Theoretically, the number is infinite, and the Fi popu- 

 lation which we have studied represents a small sample of this 

 theoretically infinite population. 



The problem that interests us is how near to the true, ab- 

 stract, theoretical statistical constants of the infinite popula- 

 tion are the constants of the sample. An indication of this is 

 obtained by calculating either the standard error or the probable 

 error, either of w^hich values gives us a measure of the reliability 

 that can be placed in the constants of the sample as indications 

 of the true values of the corresponding constants of the infinite 

 population. The probable error, the older of these two constants^ 

 states that the corresponding constant from another sample will 

 be expected to fall within certain limits in half the cases. The 

 standard error states similarly that the corresponding constant 

 of another sample will fall within certain limits in about two 

 cases out of three. The probable error is perhaps slightly more 

 useful because it gives values for an even chance, but it involves 

 a multiplication by 0.6745 and for that reason is less used today 

 than it was twenty years ago. In Table 19, the values following 

 the zb sign are the probable errors of the various constants, 

 as the standard error was little used at the time East carried 

 out this work. 



Mean 



The arithmetical average, known in statistics as the mean or 

 arithmetic mean, is frequently characterized by the symbol x^ 

 read x-bar or bar-a:. It is determined by adding together all the 

 individuals in a population and dividing the sum by the number 

 of individuals, usually designated by the symbol n. Let us use 

 the Fi from Table 19 for an example. This Fi population con- 

 sists of 46 individuals, but we find that many of them have the 

 same value. Four plants have corollas 37 mm long, and it is 

 simpler to multiply the 37 by 4 than it is to add 37 four times; 



