### Prof. Dr. Christian Wolkersdorfer

# Calculation of the mean value of pH measurements

When calculating the mean from pH value measurements, errors commonly occur. These can be attributed to the fact that the logarithmic character of the pH measurement is often not taken into account. The unitless pH value represents the negative decadic logarithm of the hydrogen ion (proton) activity:

pH = –log_{10}{H^{+}}

Consequently, the mean or average value cannot be calculated as with other measured variables, but the pH value must first be converted into the activity of the hydrogen ions (“protons”). It can be assumed that the mean value of a population is calculated, i.e. that the standard deviation is small and that there are no measured values of different populations in the low and high pH range.

When using the mean for the pH, you should always indicate, which method you used: the *arithmetic mean* or the *proton activity mean*.

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