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Calculation of the geometric mean using beach water data

This information is provided to assist operators of public and semi-public beaches and Boards of Health in interpretation of the water testing standards.

Updated May 2019

The following information is provided to assist operators of public and semi-public beaches and Boards of Health in interpretation of the water testing standards in 105 CMR 445.000: Minimum Standards for Bathing Beaches (State Sanitary Code, Chapter VII).  Additional information is available on our website at www.mass.gov/dph/beaches or by contacting the Environmental Toxicology Program at (617) 624-5757 or dph-beach@state.ma.us.

Under 105 CMR 445.031, beach water quality must meet both the single sample and the geometric mean1 (geomean) standards.  Single sample results are intended to represent current conditions while the geomean is intended to reflect typical water quality found during the preceding time period (typically a month).  This document is meant to clarify the calculation and application of the geomean.

Calculation Inputs

  • The calculation of the geomean must include the most recent five (5) results collected in the same year. This includes samples impacted by rainfall. 
  • The calculation may not include more than two samples collected on the same day, and any same-day samples must be collected at least four hours apart.  This requirement will ensure that samples represent a reasonable timespan that is representative of variations in water quality due to changes in tides, weather, swimmers, etc., while ensuring that beach operators have some flexibility.

Calculation Approach

  • We recommend that Boards of Health and beach operators utilize statistical software or free online tools when calculating the geomean. 
  • An online calculator is currently available on the website here: http://www.graftacs.com/geomean.php

1The geometric mean is the nth root of the product of a set of numbers.  For example, to calculate this type of average you would multiply the numbers together and then take a square root (for two numbers), cube root (for three numbers), etc.

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