38 



Records of the Indian Museum. 



We can now find the probable error of P. 

 shown that 



[Voi,. XXIII, 



Pearson 1 has 



cr- 



ane! 



a 



X-2 



= {2(q-l) + q/H + q(q-l)/N} 



oy* = 42-1237. Giving i°- x 2 = 3-245 



P 19 = -2030 and P n = -i226 



<T p =0*2609. 



P =-2030+1760. 



where q- number of cells and H = harmonic mean of expected 

 frequency. 



In the present case, 2 = 19, A r = 2oo, ^^ = 4*4137. 

 Hence, 

 also 



thus 



we get finally, 



The chances are 4 to 1 against its being a random sample. 

 In other words about once in five trials we would get worse 

 fits than this. The probable error of P is large. Still the fit is 

 not very bad, for odds of 4 to 1 cannot be considered excessive. 



We notice that the contributions of the terminal ranges to 

 X 1 is heavy, being 3*265, 1-504 and -482. Combining the two 

 terminal groups at each end we find x 2 = 18-482, and ri 17. We 

 get P = '2gy8 which gives a decent fit. In three trials out of ten, 

 random sampling would give us worse fits. 



Mean = 1656-25 mm. 

 S.D. = 67-3849 mm, 



Table 3. 



Unit of grouping =50 mm. 





Observed 



Theoretical 







Stature in mm. 



Value 



Value 



(m' — m). 



(m'—m) 2 





m'. 



m. 





m 



Beyond 1530 



8 



6-0993 



1*9007 



•5902 



1 53°— 1580 

 — 1630 



14 



19-6830 



5-6830 



1 '6408 



45 



43-9045 



1*0955 



•0231 



— 1680 



60 



57-8639 



2-1361 



•0788 



— 1730 



48 



45-0741 



2-9259 



•1800 



— 1700 



20 



20-7464 



0*7464 



•0268 



Beyond 1780 



5 



6-6292 



1-6292 



•4002 





200 



200*0004 



n' = ? 



.1-2=2-8399 



From Tables by interpolation, we get 



P = o-82 65 83 + -28 86 86 

 the probable error, is large, but a high value of P is not improbable. 

 I1k lit is now excellent. In 83 trials -out of 100 the At- 

 will be worse than this. We conclude therefore thai with 5 o mm. 

 Mping, the Gaussian curve is quite adequate for purposes of gra- 

 duation With this unit of grouping we may then safely investi- 



1 Phil. Mag. Vol. I.I I, 1916, pp. 369-378 



