e pass upward
into the step .90 of the total distance (1.07 units), we shall arrive at
a point .96 units (.90 x 1.07 = .96) above the lower limit of step 3,
which we find from the table is 3.15. Adding .96 to 3.15 gives 4.11 as
the median point of this eighth grade distribution.

The median and the percentiles of any distribution of scores on the
Hillegas scale may be determined in a manner similar to that illustrated
above, if the scores are assigned to the individual papers according to
the directions outlined above.

A similar method of calculation is employed in discovering the limits
within which the middle fifty per cent of the cases fall. It often seems
fairer to ask, after the upper twenty-five per cent of the children who
would probably do successful work even without very adequate teaching
have been eliminated, and the lower twenty-five per cent who are
possibly so lacking in capacity that teaching may not be thought to
affect them very largely have been left out of consideration, what is
the achievement of the middle fifty per cent. To measure this
achievement it is necessary to have the whole distribution and to count
off twenty-five per cent, counting in from the upper end, and then
twenty-five per cent, counting in from the lower end of the
distribution. The points found can then be used in a statement in which
the limits within which the middle fifty per cent of the cases fall.
Using the same figures that are given above for scores in English
composition, the lower limit is 2.64 and the limit which marks the point
above which the upper twenty-five per cent of the cases are to be found
is 5.08. The limits, therefore, within which the middle fifty per cent
of the cases fall are from 2.64 to 5.08.

It is desirable to measure the relationship existing between the
achievements (or other traits) of groups. In order to express such
relationship in a single figure the coefficient or correlation is used.
This measure appears frequently in the literature of education and will
be briefly explained. The formula for finding the coefficient of
correlation can be understood from examples of its application.

Let us suppose a group of seven individuals whose scores in terms of
problems solved correctly and of words spelled correctly are as
follows:[33]

======================================
INDIVIDUALS|No. OF |No. OF WORDS
MEASURED |PROBLEMS|SPELLED CORRECTLY
CORRECTLY | |
-----------+--------+-------