If there are X 1 ,X 2 ,,X n observations, the geometric mean, an alternative measure of

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If there are X1,X2,…,Xn observations, the geometric mean, an alternative measure of centrality, is

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For example, beach water quality is frequently assessed through the geometric mean. Below are water quality sample results collected by the Department of Health and Mental Hygiene at (Center) Manhattan Beach in New York on August 2017. Measurements are in most probable number per 100 ml (MPN / 100 ml):

60 320 100 110 48 4

a) Find the geometric mean.
b) Suppose the authorities have a standard stating that if the geometric mean of six consecutive measurements is 200 MPN/ 100 ml, that part of the beach should be closed. According to the result above, should they close the beach?

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