covered by *_n/2_
measures. For example, if the distribution contains 20 measures, the
median is that point on the scale which marks the end of the 10th and
the beginning of the 11th measure. If there are 39 measures in the
distribution, the median point is reached by counting out 19-1/2 of the
measures; in other words, the median of such a distribution is at the
mid-point of that fraction of the scale assigned to the 20th measure.

The _median step_ of a distribution is the step which contains within it
the median point. Similarly, the _median measure_ in any distribution is
the measure which contains the median point. In a distribution
containing 25 measures, the 13th measure is the median measure, because
12 measures are greater and 12 are less than the 13th, while the 13th
measure is itself divided into halves by the median point. Where a
distribution contains an even number of measures, there is in reality no
median measure but only a median point between the two halves of the
distribution. Where a distribution contains an uneven number of
measures, the median measure is the (_n_+1)/2 measurement, at the
mid-point of which measure is the median point of the distribution.

Much inaccurate calculation has resulted from misguided attempts to
secure a _median point_ with the formula just given, which is applicable
only to the location of the _median measure_. It will be found much more
advantageous in dealing with educational statistics to consider only the
median point, and to use only the _n_/2 formula given in a previous
paragraph, for practically all educational scales are or may be thought
of as continuous scales rather than scales composed of discrete steps.

The greatest danger to be guarded against in considering all scales as
continuous rather than discrete, is that careless thinkers may refine
their calculations far beyond the accuracy which their original
measurements would warrant. One should be very careful not to make such
unjustifiable refinements in his statement of results as are often made
by young pupils when they multiply the diameter of a circle, which has
been measured only to the nearest inch, by 3.1416 in order to find the
circumference. Even in the ordinary calculation of the average point of
a series of measures of length, the amateur is sometimes tempted, when
the number of measures in the series is not contained an even number of
times in the sum of their values, to carry the quotient out t