----------
A | 1 | 2
B | 2 | 4
C | 3 | 6
D | 4 | 8
E | 5 | 10
F | 6 | 12
G | 7 | 14
======================================

From such distributions it would appear that as individuals increase in
achievement in one field they increase correspondingly in the other. If
one is below or above the average in achievement in one field, he is
below or above and in the same degree in the other field. This sort of
positive relationship (going together) is expressed by a coefficient of
+1. The formula is expressed as follows:

(Sum x . y)
r = ------------------------------
(sqrt(Sum x^2))(sqrt(Sum y^2))

Here _r_ = coefficient of correlation.

_x_ = deviations from average score in arithmetic (or difference between
score made and average score).

_y_ = deviations from average score in spelling.

Sum = is the sign commonly used to indicate the algebraic sum (_i.e._
the difference between the sum of the minus quantities and the plus
quantities).

_x . y _= products of deviation in one trait multiplied by deviation in
the other trait with appropriate sign.

Applying the formula we find:
===================================================================
|ARITH-| | | SPEL- | | | |
|METIC | x | x^2 | LING | y | y^2 | x.y |
--+------+---+------------+-------+---+-------------+-------------+
A | 1|-3 | 9| 2|-6 | 36| +18|
B | 2|-2 | 4| 4|-4 | 16| +8|
C | 3|-1 | 1| 6|-2 | 4| +2|
D | 4| 0 | 0| 8| 0 | | |
E | 5|+1 | 1| 10|+2 | 4| +2|
F | 6|+2 | 4| 12|+4 | 16| +8|
G | 7|+3 | 9| 14|+6 | 36| +18|
| ___| | __| ___| | ___| __|
| 7 |28| |Sum x^2 = 28| 7 |56| |Sum y^2 = 112|Sum x.y = +56|
|Av. =4| | |Av. =8 | | | |
===================================================================
Sum x . y +56 +56
r = ---------------------------- = -