GEOMETRIC MEAN and Properties
The geometric mean in statistics takes on particular importance when we want to calculate an average rate over a certain time period.
To calculate the geometric mean, we'll use the product rather than the sum, and instead of dividing by n as we did for the arithmetic mean, here we'll square everything with the index n.
To calculate the weighted geometric mean, we'll consider the absolute frequencies and use them as exponents.
Finally, we'll look at the properties of the geometric mean, including its logarithmic property.
IMPORTANT: The logarithm I use in the video is the natural logarithm, not the decimal logarithm. To calculate the natural logarithm, use the "ln" key on your calculator. The exponential function exp, on the other hand, is calculated on your calculator using the "e to the power of x" key. DO NOT USE THE EXP KEY!!! I REPEAT: THE EXP KEY DOES NOT CALCULATE THE EXPONENTIAL FUNCTION! e^x does.
In any case, the same property explained in the video also applies to the decimal logarithm and with the antilog replacing exp. The decimal logarithm is calculated using the "log" key, while the antilog is calculated using the "10 to the power of x" key.
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0:00 Last property of the arithmetic mean
1:00 Geometric mean: simple case
3:12 Geometric mean: weighted case
4:22 Property of the geometric mean
6:39 Exam questions with solutions
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