RESPIRA TION. 129 



The problem is to find the value of the median measure- 

 ment or the median value. There are 158 values below 

 the median and as many above. 



First. To locate the median observation : This is equiv- 

 alent to saying find in the lower series of numbers 

 (1-7 17, etc.) the 158th observation from either end. It 

 must be located in the pile of cards which numbers 74. 

 This group may be called the median group. But where in 

 this group is the median observation located? In order to 

 determine this, add the groups at 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. l-f-7-fl7-|-4 1 + 70= 136. To this sum one 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. 



Second. 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 the median value 

 would be 56ff cm. 



Let us put a general proposition in the form of an al- 

 gebraic formula. 



Let M = the number of observations in the median 

 group. 



Let n = the total number of observations. 



2p = the sum of the plus groups. 



2m = the sum of the minus groups. 



a = the minimum value of the median group. 



d = the arithmetric difference in the minimum values 

 of the groups. 



fj. = the median value to be determined. 



d(- 2m) df-4 



Then * = a +.- O r ,* = a + d- V 2 



