Tlic Degree of Accuracy of Statistical Data 7 



and 



2^2 — 3/?i — 6=. I I 22>0, 



or we have a curve of type IV. 



Proceeding to determine the other constants, we find : 



r=iii.9. 

 v=iio.4 (v is positive since /i.3 is negative. Professor Pearson gets 

 these interchanged), 



« = 7.i55 ^. = 56.99. 



Distance of origin from ccntroid vertical=7.o57. 



log _>/o= 18.0822. 



Thus the equation of the curve is 



•^"=7-i55 tan $. 



Professor Pearson's constants, obtained by the aid of seven- 

 place logarithm tables are 



. /Jt2=. 910906 /3i=. 072222 



i^3=.2339o8 /32=3- 164684 



/U4=2. 625896 2/82 — 3/?i — 6=. 1 12702 



r=iii.398 a=7.i66i3 



v= 109. 047 ^=56.699 



Distance of origin from centroid vertical — 7.0149, 



logj'<,=l8'.443i056, 

 whence the equation of the curve is 



y=-y^ COS^13.398^^109.0470_ 



;i:=7. 16613 tan 6. 



Tlie two curves are drawn in fig. 2. A comparison of them 

 with the frequency polygon shows that not enough is gained in 

 accuracy by carrying more than four decimal figures to warrant 

 the extra expenditure of time and labor. 



Thus this problem also verifies the conclusions reached above: 

 that, in the fitting of a theoretical curve to the observations, it is 

 the height of folly to waste time and energy on needless and 



93 



