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

The sum of the squares of two consecutive integers is 145. What are the integers?

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A man rows downstream at 6 km/h and upstream at 4 km/h. What is the speed of the stream?

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

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What is the sum of all even numbers between 1 and 50?

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If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

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The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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If a:b = 2:3 and b:c = 4:5, what is a:c?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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What is the value of log₃(27)?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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