If the measuring instrument has been carefully derived and accurately scaled, however, it is often desirable, especially where the group being considered is reasonably large, to locate the exact point within the step on which the median falls.  If the unit of the scale is some measure of the variability of a defined group, as it is in the majority of our present educational scales, this median point may well be calculated to the nearest tenth of a unit, or, if there are two hundred or more individual measurements in the distribution, it may be found interesting to calculate the median point to the nearest hundredth of a scale unit.  Very seldom will anything be gained by carrying the calculation beyond the second decimal place.

The best rule for locating the median point of a distribution is to take as the median that point on the scale which is reached by counting out one half of the measures, the measures being taken in the order of their magnitude.  If we let n stand for the number of measures in the distribution, we may express the rule as follows:  Count into the distribution, from either end of the scale, a distance 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.