60 The Ojjsonic Index — A Medico- Statistical Enquiry 
are the leucocytes and the character the amount of phagocytosis. We set this 
forth by stating the number of leucocytes in a count say of 100 which possess the 
varying numbers of bacteria. 
Number of ) 
leucocytes j 
12 
16 
22 
17 
11 
6 
5 
3 
3 
2 
1 
1 
1 
Totals 
100 
Number of con- \ 
tained bacteria J 
0 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
311 
The number of leucocytes which contain no bacteria is 12 ; those containing one 
bacterium are sixteen, and so on. If now we plot in the usual way number of 
leucocytes against number of contained bacteria we get, when we join up the tops 
of all the ordinates, what is called a frequency polygon. 
0 1 2 3 4 5 6 7 8 9 10 11 12 
Fig. 1. Frequency Polygon. 
The way in which the numbers gradually increase and then gradually decrease 
suggests that we might be able to replace the polygon with a mathematical curve 
expressing what is the degree of phagocytosis under the conditions of experiment. 
But if we counted a second, a third and further hundreds from our slide, we should 
find that the frequency distribution was never twice the same. We might then 
be in a position to realise to what extent our method was only a rough approxi- 
mation to the true state of affairs. We might take very naturally the usual form 
of average — the Arithmetic Mean — and say we shall deal only with averages of 
distributions and so get over the difficulty of this variation in our data. But we 
find that in so doing we have exactly the same difficulty to contend with ; the 
averages, as determined from successive samples taken from the same material, 
vary just Hke the distributions. And yet we cannot help feeling that a definite 
