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

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

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What is the greatest common divisor (GCD) of 36 and 48?

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If x^2 - 5x + 6 = 0, what are the roots?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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The probability of rolling a sum of 7 with two dice is:

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If 2x = 16, what is the value of x?

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What is the remainder when 5^100 is divided by 3?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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