APPENDIX 



689 



abscissa of the center of gravity of the total area under the curve is the 

 mean of the population, and the abscissa of the highest point on the fre- 

 quency curve is the theoretical mode of the population. 



FIG. 2 



Graph of a mathematical function. A number^ is said to be a mathematical 

 function of a number x if to assigned values of x there correspond definite 

 values oiy. 



Thus, if y 2.x,y\s a function of x, 

 since for any assigned value of x we 

 can compute y. In general, if x and_y 

 are connected by an equation each is a 

 function of the other. The study of 

 certain functions is of the first rate in 

 importance in the mathematical theory 

 of statistics, and this is much facili- 

 tated by the use of the graph of the X" 

 function in question. We therefore 

 proceed to show how to form the graph 

 of a few simple functions so as to 

 give the general notion of the graph 

 of functions. 



Take coordinate axes, as in Fig. 3, 

 which divide the plane into four quad- 

 rants. If the abscissas are positive, FIG. 3 

 they should be laid off to the right 



of O ; if negative, they should be laid off to the left of O. The ordinates, if 

 positive, are to be laid off upward from the ^r-axis ; if negative, they are to be 

 laid off downward. Then whatever two numbers (positive or negative) are 

 given as abscissa and ordinate, the corresponding point can be located. 



