What is the effect of change of origin and scale on geometric mean?

The geometric mean is sensitive to changes in scale and origin. When the scale of the data changes (e.g., multiplying all values by a constant), the geometric mean is also multiplied by that constant, reflecting the change in scale. However, changing the origin (e.g., adding or subtracting a constant from all values) does not affect the geometric mean, as it relies on the multiplicative relationships between values rather than their absolute positions. Thus, only changes in scale impact the geometric mean, while changes in origin have no effect.