Appendix E 405 



number of individuals. The formula for the operation is * 



n 



Thus in our problem it would be found as shown in the table : 



V f D Df 



9.5 x 4 28.44 113.76 



19.5 x 72 18.44 1327.68 



29.5 x 169 8.44 1426.36 



39.5 x 125 1.56 195.00 



. 49.5 x 64 11.56 739.84 



59.5 x 38 21.56 819.28 



69.5 x 11 31.56 347.16 



79.5 x 11 41.56 457.16 



89.5 x 6 51.56 309.36 



5735.60 



5735 ' 60 = 11.4712cm. 

 500 



Of course, the deviations below the mean (28.44, 18.44, 8.44) 

 are negative quantities, those above (1.56, 11.56, 21.56, 31.56, 

 41.56, 51.56) positive, but inasmuch as we are here concerned 

 only with deviation from type, we are correct in neglecting these 

 signs, and using the arithmetic sum, and not the algebraic. 



We would secure the same result if we went along our line 

 of bean plants spoken of above with an average or mean indi- 

 vidual as a measure, added up the lengths by which each one 

 missed of being an average individual, and then divided this 

 total by 500, the number of individuals measured. Clearly this 

 would give the amount by which, on the average, each individual 

 missed of being the mean or the average individual. 



Standard deviation. Another constant expressing departure 

 from type, and one which is preferred by biometricians on mathe- 

 matical grounds, is standard deviation, designated by the Greek 

 letter small "sigma " (<r). It is found by squaring the deviations 

 from the mean before multiplying by the frequencies, dividing 

 the summation of these products by the number of individuals. 



