In what situations is the geometric mean preferred over the arithmetic mean?

The geometric mean is preferred when dealing with ratios, percentages, or values that are multiplicative in nature, such as growth rates.

What is the geometric mean of 2 and 8?

The geometric mean of 2 and 8 is: $$\text{GM} = \text{sqrt}(2 \times 8) = \text{sqrt}(16) = 4$$ .

If the geometric mean of two numbers is 5, what can you say about the numbers?

If the geometric mean is 5, then the product of the two numbers is: $$\text{GM}^2 = 5^2 = 25$$ .

How do you find the geometric mean of a set of n numbers?

To find the geometric mean of n numbers, multiply all the numbers together and take the n-th root: $$\text{GM} = \text{sqrt[n]}(x_1 \times x_2 \times ... \times x_n)$$ .

What is the geometric mean of 5 and 20?

The geometric mean of 5 and 20 is: $$\text{GM} = \text{sqrt}(5 \times 20) = \text{sqrt}(100) = 10$$ .

What is the formula for the geometric mean of two variables x and y?

The formula for the geometric mean of two variables x and y is: $$\text{GM} = \text{sqrt}(x \times y)$$ .

If the geometric mean of two numbers is 6, what are the possible pairs of numbers?

Possible pairs of numbers could be (4, 9), (3, 12), or (1, 36), as long as their product equals 36.

What is the geometric mean of 10 and 50?

The geometric mean of 10 and 50 is: $$\text{GM} = \text{sqrt}(10 \times 50) = \text{sqrt}(500) = 10\text{sqrt}(5)$$ .

Flashcard

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Mathematics

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9th - 12th Grade

•

Practice Problem

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Hard

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CCSS

8.EE.A.2

Standards-aligned

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FLASHCARD QUESTION

Front

What is the geometric mean of two numbers a and b?

Back

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

How do you calculate the geometric mean of three numbers a, b, and c?

Back

FLASHCARD QUESTION

Front

What is the relationship between the arithmetic mean and the geometric mean?

Back

FLASHCARD QUESTION

Front

If the geometric mean of two numbers is 12, what is the product of those two numbers?

Back

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

What is the geometric mean of 4 and 16?

Back

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

How do you express the geometric mean in terms of logarithms?

Back

Tags

CCSS.8.EE.A.2

FLASHCARD QUESTION

Front

What is the geometric mean of 1, 3, and 9?

Back

Tags

CCSS.8.EE.A.2

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