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Answer :
To find the geometric mean of a set of numbers, you multiply all the numbers together and then take the nth root of the product, where n is the total number of values in the set.
Let's break down the steps to find the geometric mean for each set of values:
Set X: 12, 18, 48, 61
Multiply all the numbers together:
[tex]12 \times 18 \times 48 \times 61 = 635, 040[/tex]
Since there are 4 numbers, take the 4th root of the product:
[tex]\text{Geometric Mean} = \sqrt[4]{635,040} \approx 29.54[/tex]
Set Y: 5, 3, 2, 8
Multiply all the numbers together:
[tex]5 \times 3 \times 2 \times 8 = 240[/tex]
Again, since there are 4 numbers, take the 4th root of the product:
[tex]\text{Geometric Mean} = \sqrt[4]{240} \approx 4.34[/tex]
The geometric mean provides a measure of central tendency that is especially useful for comparing numbers on vastly different scales or when dealing with percentages, rates, or indices.
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