THE PROBABLE ERROR OF THE MEAX. 13 



The manner of calculating the probable error of the mean 

 is quite simple. Having calculated the mean of all deter- 

 minations, we find the differences between this mean and 

 every single determination. We square each one of these 

 differences, and take the sum of these squares. 



Next we multiply the number of determinations by the 

 next lower number. The sum of the squares is divided by 

 this product. 



Two-thirds of the square root of the quotient thus 

 obtained is the probable error of the mean. 



It may be necessary to give an example in full detail of 

 this calculation of the probable error of a mean. Let us 

 take the 20 silver dollars weighed on April 4, 1901. 



The year of coinage of each silver dollar and its weight 

 (in grammes and centigrammes) is given in the first two 

 columns. 



The mean 26.51 gives the difference expressed in centi- 

 grammes in the next column. The fourth column gives the 

 square of each of these differences. 



