Topic Details (Notes format)

How to Calculate Arithmetic Mean, Geometric Mean, and Harmonic Mean

Subject: Mathematics

Book: Maths Mastery

While the arithmetic mean is the familiar (sum ÷ count), the geometric mean multiplies data points and takes the nth root, and the harmonic mean deals with reciprocals. For numbers a and b, the geometric mean is √(ab), while the harmonic mean is 2 ÷ (1/a + 1/b). Each mean highlights different aspects of datasets, with the harmonic mean particularly relevant for rates (speed, frequency) and the geometric mean for growth processes (like interest rates). Understanding the trio fosters nuanced data analysis, ensuring you pick the correct mean to represent your dataset or scenario accurately.

Practice Questions

If the product of two numbers is 120 and their sum is 26, what are the numbers?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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What is the sum of the interior angles of a hexagon?

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What is the probability of drawing a king from a standard deck of 52 playing cards?

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If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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