A set of numbers is transformed by taking the log base 10 of each number. The mean of the transformed data is 1.65. What is the geometric mean of the untransformed data?

Step-by-step explanation:

Given that:

A set of numbers is transformed by taking the log base 10 of each number. The mean of the transformed data is 1.65. What is the geometric mean of the untransformed data.

To obtain the geometric mean of the untransformed data,

X = set of numbers

N = number of observations

Arithmetic mean if transformed data = 1.65

Log(Xi) = transformed data

Arithmetic mean = transformed data/ N

Log(Xi) / N = 1.65

(Πx)^(1/N), we obtain the antilog of the aritmétic mean simply by raising 10 to the power of the Arithmetic mean of the transformed data.

10^1.65 = 44.668359

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