690 



APPENDIX 



Let us take as an illustration the plotting of the graph of y = 2.x + 4. 

 Here we see from the equation that corresponding to any value assigned 

 to x we get a value of y equal to twice x plus 4. The corresponding values 

 are as follows : 



Locating, in Fig. 3, the points corresponding to these values, and draw- 

 ing a smooth curve through them, we have the graph of the function. This 

 graph is a straight line. 



We leave as an exercise for the student to find the graph of y = x z . For 

 application of graph of function, see "Probability Curve," Section VI. 



SECTION IV "SMOOTHING" OF FIGURES 



Sometimes the frequency distribution of a population arranged with 

 respect to some character has many small irregularities which arise merely 

 from the way in which the measurements were taken and grouped. In 

 such a case a process called "smoothing" can often be employed to 

 obtain regularity. A noteworthy instance of smoothing is to be seen in the 

 adjusting of the population census with respect to age, there being a great 

 many more people who report their ages as 40 than as 39 or 41. In 

 fact, sometimes the unsmoothed figures show one half more people of 

 age 40 than of age 39 or 41. It is, then, manifestly desirable to smooth 

 these census returns if they are to give even an approximately correct 

 impression. 



In representing such a distribution graphically we have to draw a smooth 

 line in the neighborhood of the points, but not necessarily through any of 

 them. This smooth line is the result of the attempt to present what the 

 distribution would be if the causes of the small irregularities could be 

 removed. Sometimes it is convenient to smooth figures without resorting 

 to a graph. There are some rather refined but complicated algebraic 

 methods l of doing this, but in general a very simple method can be used. 

 To explain this method, take the following frequency distribution (which 

 was obtained by measuring the circumferences of 995 ears of corn), in which 

 the groupings into |-inch classes are not well selected. 



1 Darwin, Philosophical Magazine and Journal^ July, 1877. 



