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Questions and Answers
What is the geometric mean of the set of numbers {1, 2, 3, 4, 5}?
What is the geometric mean of the set of numbers {1, 2, 3, 4, 5}?
Which of the following statements is true about the geometric mean?
Which of the following statements is true about the geometric mean?
What is the geometric mean of the set of numbers {2, 4, 8}?
What is the geometric mean of the set of numbers {2, 4, 8}?
In which of the following fields is the geometric mean used to calculate the average rate of return on an investment?
In which of the following fields is the geometric mean used to calculate the average rate of return on an investment?
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What is the formula for calculating the geometric mean of a set of n numbers?
What is the formula for calculating the geometric mean of a set of n numbers?
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What is the geometric mean of the set of numbers {10, 20, 30}?
What is the geometric mean of the set of numbers {10, 20, 30}?
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Study Notes
Geometric Mean
Definition: The geometric mean is a type of average that is used to calculate the central tendency of a set of numbers by using the product of their values.
Formula: The geometric mean of a set of n numbers {x1, x2, ..., xn} is calculated as:
gm = √(x1 × x2 × ... × xn)
Alternative Formula: The geometric mean can also be calculated using the following formula:
gm = e^(∑(ln(x)) / n)
where ln is the natural logarithm.
Properties:
- The geometric mean is always less than or equal to the arithmetic mean.
- The geometric mean is sensitive to the units of measurement.
- The geometric mean is used to calculate the average of rates, ratios, and indexes.
Applications:
- Finance: The geometric mean is used to calculate the average rate of return on an investment.
- Economics: The geometric mean is used to calculate the average growth rate of an economy.
- Engineering: The geometric mean is used to calculate the average rate of flow in a system.
Examples:
- The geometric mean of the numbers {2, 4, 8} is √(2 × 4 × 8) = 4.
- The geometric mean of the numbers {10, 20, 30} is e^(∑(ln(x)) / 3) = 20.
Geometric Mean
- The geometric mean is a type of average that calculates the central tendency of a set of numbers using the product of their values.
Formula
- The geometric mean of a set of n numbers {x1, x2,..., xn} is calculated as gm = √(x1 × x2 ×...× xn).
- The geometric mean can also be calculated using the alternative formula: gm = e^(∑(ln(x)) / n).
Properties
- The geometric mean is always less than or equal to the arithmetic mean.
- The geometric mean is sensitive to the units of measurement.
- The geometric mean is used to calculate the average of rates, ratios, and indexes.
Applications
- In finance, the geometric mean is used to calculate the average rate of return on an investment.
- In economics, the geometric mean is used to calculate the average growth rate of an economy.
- In engineering, the geometric mean is used to calculate the average rate of flow in a system.
Examples
- The geometric mean of the numbers {2, 4, 8} is √(2 × 4 × 8) = 4.
- The geometric mean of the numbers {10, 20, 30} is e^(∑(ln(x)) / 3) = 20.
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Description
Learn about the geometric mean, a type of average used to calculate the central tendency of a set of numbers. Understand its formula, alternative formula, and properties.
