The median initial data analysis

Determining the median of a set of experimental results usually requires little or no calculation. Moreover, in many cases it may be a more realistic measure of central tendency than the arithmetic mean. 

Determine the mean and the median for the following four titration values. 25.01, 25.04, 25.06, 25.21 ml 

It is easy to calculate that the mean of these four observations is 25.08 ml, and that the median - in this case the average of the second and third values, the observations already being in numerical order - is 25.05 ml. The mean is greater than any of the three closely-grouped values (25.01, 25.04 and 25.06 ml) and may thus be a less realistic measure of central tendency than the median. Instead of calculating the median we could use the methods of Chapter 3 to test the value 25.21 as a possible outlier, and determine the mean according to the result obtained, but this approach involves extra calculation and assumes that the data come from a normal population. 

This simple example illustrates one valuable property of the median it is unaffected by outlying values. Confidence limits (see Chapter 2) for the median can be estimated with the aid of the binomial distribution. This calculation can be performed even when the number of measurements is small, but is not likely to be required in analytical chemistry, where the median is generally used only as a rapid measure of an average. The reader is referred to the bibliography for further information. 

In non-parametric statistics the usual measure of dispersion (replacing the standard deviation) is the interquartile range. As we have seen, the median divides the sample of measurements into two equal halves if each of these halves is further divided into two the points of division are called the upper and lower quartiles. Several different conventions are used in making this calculation, and the interested reader should again consult the bibliography. The interquartile range is not widely used in analytical work, but various statistical tests can be performed on it. 

---