Interquartile range normalization, data

Interquartile range The middle 50% of a set of data arranged in ascending order. The normalized interquartile range serves as a robust estimator of the standard deviation. (Section 2.6.2)... 

If you are concerned that the data are not normally distributed or have extreme outliers, robust estimators such as the median and interquartile range may be more useful. (Section 2.6)... 

The interquartile range is the middle 50% of the data. As there are 25 data points we take the middle 13 from 0.1142 to 0.1155 which gives an interquartile range of 0.0013 M. Therefore the normalized interquartile range is 0.0013 x0.75 = 0.00098 M. 

For the RACI titration competition data the median is 0.1146M and the normalized interquartile range is 0.00098 M. 

Because the use of a sample mean, and particularly a sample standard deviation, relies on the assumption of normality of distribution of the data, outliers in the data must be suitably dealt with. Alternatively, robust z-scores may be calculated from the median and the normalized interquartile range (norm IQR). 

A simple robust estimate of the standard deviation is provided by the interquartile range (IQR, see Section 6.2). For a normal error distribution, the IQR is ca. 1.35standard deviation estimate that is not affected by any value taken by the largest or smallest measurements. Unfortunately, the IQR is not a very meaningful concept for very small data sets. Moreover, and somewhat surprisingly, there are several different conventions for its calculation. For large samples the convention chosen makes little difference, but for small samples the differences in the calculated IQR values are large, so the IQR has little application in analytical chemistry. 

That the robust measures are less sensitive to outliers than the classical measures discussed before can be seen in a simple example. Suppose that the data we consider are the integers from 6 to 6, excluding 0. (These numbers are chosen only for a simple illustration of the principle, and, in particular, do not follow a normal distribution.) The mean is 0, and interquartile range of 7. Imagine now that by mistake 6 is replaced by 16. The mean becomes 0.83, and ax5.73. However, median and interquartile range are unchanged. 

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