116 DOMESTICATED ANIMALS AND PLANTS 
error, it may be called an even 7 the next time it occurs. The 
only trouble with this plan is the difficulty of keeping account 
of the many assignments. It is much easier to always put them 
in the class above (or below, if the worker prefers), but a slight 
error is introduced, affecting, of course, the mean, to raise or to 
lower it, though ever so slightly. In all but the best work it is 
better to admit this error than to keep an accurate account of 
the alternate assignment of the midclass measurements. 
One more caution must be mentioned in connection with 
grouping measurements. Suppose we have a series running, we 
will say, as follows: 10, 11, 12, 13, etc., up to 50. If now we take 
them as they are, there will be some forty-one different groups, 
involving immense and unnecessary labor. The thing to do is to 
combine them into fewer groups, but in doing so it is important 
to observe great care in choosing the scheme for grouping. 
For example, suppose we attempt to group them as follows: 
10, 14, 18, 22, etc., reducing them to one fourth of the original 
number. What, now, will be the result ? Consider the numbers, 
for instance, between 14 and 18. What is to be done with them? 
That is, how are the numbers represented by 15, 16, and 17 to 
be recognized in our new scheme? It will be noticed at once 
that we have chosen a scheme with ¢Aree values between. Of 
these three values, 15 will of course go down with its new class 
mark, 14; and 17 will go up to 18. But what is to become of 
16? Whichever way we put it the result will be to distort the 
distribution and prevent its being smooth ; that is, it will put 
sudden humps and high spots into it, like saw teeth, that arise 
not from the variability in the true measurements but in the 
error introduced in the manner of grouping them. 
The better way would be to choose a new scheme with an 
even number between the new values. For example, suppose 
we choose the following: 10, 15, 20, 25, 30, etc. Now there 
are four values between 20 and 25, namely, 21, 22, 23, 24, of 
which two can go up to 25 and two go down to 20, thus keep- 
ing true relative values and insuring a smooth distribution. 
