Porter — The Growth of St. Louis Children. 281 
If the number of observations is very large, the MEAN 
(MEDIAN value, M,) may be found with considerable accuracy 
by a mere inspection of the series. The mean of such a 
series is the measurement which most frequently recurs. 
Thus, the mean height of the recruits of Table No. 2, page 278, 
is between 67 and 68 inches. The accuracy with which the 
mean can thus be found depends not only on the number of ob- 
servations, but also on the size of the units of measurement. 
For most purposes it is desirable to know not merely at 
which inch, centimetre, kilogramme or other unit the greatest 
number of observations is found, but exactly at what fraction 
of the unit. Again, the relation between the number of 
observations and the size of the unit may be such that 
the largest number of observations at one unit will not 
fall at the true mean, or line dividing the total number 
of observations into two equal groups. The method by 
which the mean can be calculated with exactness will be 
illustrated by the following example. The mean height of 
the girls in Table No. 4 is obtained by adding the number 
of observations from below upwards until the sum cannot 
be increased by the next number in the column without 
exceeding half of the total number of observations. Thus 
1046 is reached opposite 123 cm.; the next number in 
the column (141) would make the sum 1187, which is 
more than the half (1061) of the total number of observa- 
tions (2122). The mean is, therefore, greater than 123 cm. 
but less than 125 cm. Its position is found by interpolation. 
Half of the total number of observations is 1061, which is 15 
more than the sum of the observations up to 124 em.; 15 is 
11 per cent. of 141, the observations at 124 cm. Hence, the 
mean is 124.15 cm. 
Neither the mean nor the average can give any information 
as to the way in which the individual observations in a series 
are distributed, and it is plain that two series having an iden- 
tical mean or average may differ greatly in respect of the 
dispersion of the individuals from the middle value. Thus the 
two very different series — 
4, 5, 6, 14, 15, 16 
¥, 0, 10, 10,11; 71 
