## Choice of method to calculate quantiles

The method described in the BS EN 13795-1:2019 (A.3 Treatment of results) to calculate upper and lower quartile results is not well established or available in common software  packages. Consequently SMTL use the Hyndman and Fan (Rob J Hyndman and Yanan Fan, 1996, American Statistician 50 361-365 "Sample Quantiles in Statistical Packages" - PDF) definition 7 method to calculate the lower and upper quartile test results as this is a method commonly used and available in  spreadsheet and statistical software (Excel, LibreOffice, Google Sheets, R and S).

## Quantile calculations for bioburden determinations with zero plate counts

BS EN 13795-1:2019 (A.2.1 Test method for evaluation of cleanliness microbial/bioburden) requires the median (Md) and upper quartile (Uq) to be reported. However, a bioburden test with zero counts on a plate is usually reported as "less than the correction factor, rounded up to the nearest whole figure".  EN 13795 is not specific about how this is dealt with when calculating quantiles.  Therefore SMTL's policy for the purposes of calculating the summary statistics for a test where one or more of the 5 plates have zero counts, is that the number to be used for zero plate counts will be the correction factor rounded to the nearest whole figure.

To give a concrete example, if the 5 plates had counts of

0 3 15 0 1

with a correction factor of 1.5, the reported counts would be:

2  4 22  2  2

Using the Hyndman and Fan definition 7 method, the quantile statistics would be as follows:

M=2

Uq=4