---+----+----+-----+-----+-----+-----++------|
| | | | | | | || |
| - 4 | .. | .. | .. | .. | .. | 1 || .. |
| - 3 | .. | .. | .. | .. | .. | .. || .. |
| - 2 | 1 | 4 | 1 | 7 | .. | 2 || 15 |
| - 1 | 2 | 7 | 7 | 28 | 15 | 4 || 63 |
| - 0 | 3 | 10 | 6 | 32 | 40 | 10 || 91 |
| + 0 | 1 | 11 | 6 | 7 | 14 | 11 || 50 |
| + 1 | 1 | 3 | 20 | 9 | 4 | 1 || 38 |
| + 2 | .. | 5 | 48 | 26 | .. | 1 || 80 |
| + 3 | .. | 1 | 32 | 36 | 2 | .. || 71 |
| + 4 | .. | 1 | 5 | 25 | 25 | .. || 56 |
| + 5 | .. | 1 | .. | 6 | 25 | .. || 32 |
| + 6 | .. | 2 | .. | 3 | 10 | .. || 15 |
| + 7 | .. | 1 | .. | .. | 14 | .. || 15 |
| + 8 | .. | .. | .. | .. | 3 | 7 || 10 |
| + 9 | .. | .. | .. | .. | 2 | 4 || 6 |
| +10 | .. | .. | .. | .. | .. | .. || .. |
| +11 | .. | .. | .. | .. | .. | 1 || 1 |
|-------+----+----+-----+-----+-----+-----++------|
| Total | 8 | 46 | 125 | 179 | 154 | 42 || 554 |
+-------------------------------------------------+

In the distribution of all the parallax stars we once more find a
similar bipartition of the stars. Arguing from these statistics some
astronomers have put forward the theory that the stars in space are
divided into two classes, which are not in reality closely related. The
one class consists of intensely luminous stars and the other of feeble
stars, with little or no transition between the two classes. If the
parallax stars are arranged according to their apparent proper motion,
or even according to their absolute proper motion, a similar bipartition
is revealed in their frequency distribution.

Nevertheless the bipartition of the stars into two such distinct classes
must be considered as vague and doubtful. Such an _apparent_
bipartition is, indeed, necessary in all statistics as soon as
individuals are selected from a given population in such a manner as the
parallax stars are selected from the stars in space. Let us consider
three attributes, say _A_, _B_ and _C_, of the individuals of a
population and suppose that the attribute _C_ is _positively_ correlated
to the attributes _A_ and _B_, so that to great or small values of _A_
or _B_ correspond respectively great or small values of _C_. Now if the
individuals in the population are statistically selected in such a way
that we choose out indi