116 



SPECIAL PHYSIOLOGY 



having 52 cm., and so on. In the case in question it was found that 

 the 316 cards were quickly distributed, falling into the following 

 groups : 



The problem is to find the value of the median measurement or 

 the median value. There are 158 values below the median value 

 and as many above it. 



1. To Locate the Median Observation. This is equivalent to saying 

 find in the lower series of numbers (1-7-17, etc.) the 158th observa- 

 tion from either end. It must be located in the pile of cards which 

 number 74. This group may be called the median group. But where 

 in this group is the median observation located ? In order to deter- 

 mine this, add the groups to the left of the median group, these may 

 be called the minus groups, the values which they represent being 

 less than that of the median group: 1, 7, 17, 41, 70 =136. 



To this sum we must add 22 observations from the median group 

 to make 158. The median observation is then located in the median 

 group, 22 points from the left. 



2. To evaluate the median observation we must take it for granted 

 that the 74 observations of the median group are evenly distributed 

 over the distance between 56 cm. and 57 cm. That being the case, 



22 



the median value would be 56 and =-7 cm. 



74 



If it is desired to reduce this simple process to a mathematical 

 formula, that can readily be done: 



Let n=the total number of observations (316). 



m=the number of observations in the median group (74). 

 Z=the sum of the minus groups at the left (136). 

 r=the sum of the plus groups to the right (106). 

 a=the minimum value of the median group (56 cm.). 

 d=the arithmetical difference in the minimum values of 



the groups (1 cm.). 

 M=the median value to be determined. 



Then M = a 



orM = 5G + 





= 56 =56.3 cm. 



74 



After one has found the median value for each measurement in 

 each group, these may be tabulated and the values compared. When 

 the table of median values is large it is almost necessary to carry the 

 work of reduction a step farther and represent these values graphic- 



