Inter-quartile range

The range of the data is defined as the difference between the maximum and minimum value it is very sensitive to outliers which coincide with either the maximum or minimum or both. The robust counterpart of the range is the inter QUARTILE RANGE (IQR, X iqr). 

A second, simple measure of variability is the inter-quartile range that is the interval between the upper and lower quartiles. The upper quartile of a set of data is that value that is less than 25% of the data and greater than 75% similarly, the lower quartile is the value that is greater than 25% of the data and less than 75%. For the blood glucose data the lower quartile is 3.6 mmol / Land the upper quartile 4.55 mmol/L, giving an interquartile range of 0.95 mmol/L. 

The inter-quartile range as an indicator of dispersion The inter-quartile range is defined as the difference between the upper and lower quartiles (Q3 — Ql). So, for steroid 1 ... 

The inter-quartile range for the half life of steroid 2 is thus only half that for steroid 1, duly reflecting its less variable nature. 

Just as the median is a robust indicator of central tendency, the interquartile range is a robust indicator of dispersion. Take the longest half-life seen with steroid 1 (15.8 h) and consider what would have happened if that individual had produced a half-life of 100 h (or any other extreme value). The answer is that it would make absolutely no difference to the inter-quartile range. The value of 15.8 h is already something of an outlier, but it had no undue effect on the inter-quartile range. 

Median and inter-quartile range are robust indicators of central tendency and dispersion... 

The second quartile (median) and inter-quartile range can be used as an alternative method for describing the central tendency and dispersion of a set of measured data. Both are robust and can be useful where there are occasional extreme values. 

The spread of a distribution may be expressed in terms of a range, i.e. the difference between its minimum and maximum sizes the inter-quartile range is the difference between the 25% and 75% size (25JC75) the interpercentile range between two percentages, usually 10 and 90 ( (A9o)- The least significant of these is the first, since a stray undersize or oversize... 

Fig. 3. The mean and inter-quartile range of the capacity of HEDA networks of varying sizes and the theoretic capacity of similar HNNs (single line).

Figure 1. Median frequency of enurinalion per hour by female maras, in relation to female reproductive status. Bars show median values and vertical lines show inter-quartile ranges. Some females were sampled mote than once, at different stages of their reproductive cycles. The sum of the sample sizes for each category (n=80) is therefore greater than the actual sample size (n=41).

We now present and discuss some of the results of the benchmark. The benchmark exercise features aU of the techniques applied to each of the examples, but in the scope of this document we only can present a representative subset. Most of the graphics are shown in form of box plots derived from the 25 available runs per sample size. The box plots show the lower quartile, the median, and the upper quartile values. The whiskers in the plots are lines showing the data range. Outhers are detected using a multiple (here 3) of the inter-quartile range. 

For all the 11 questions, the following statistical parameters have been calculated mean, median, standard deviation and inter-quartile range. 

The Inter-Quartile Range (IQR) is the difference between the 3rd and 1st quartile in which lie 50% of core values. The higher the IQR, the greater the dispersion of the data. Thus, an IQR less than 1 means that more than 50% of all opinions fall at a certain point on the scale and shows that they have reached consensus (von der Gracht and Darkow, 2010). An IQR of zero indicates a perfect consensus among panel members. 

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