Topic Details (Notes format)

How to Calculate Variance and Standard Deviation

Subject: Mathematics

Book: Maths Mastery

Variance measures how spread out data values are around the mean, calculated by averaging the squared differences from the mean. Standard deviation is the square root of variance, returning the measure to the original data units. For a dataset [2, 4, 4, 6, 8], the mean is 4.8, each difference is (2 – 4.8)², (4 – 4.8)², etc., then averaged to get variance, and the square root yields the standard deviation. Higher standard deviation indicates greater spread. These metrics are fundamental in statistics, quality control, finance risk, and any field requiring data analysis. Familiarity with variance and standard deviation fosters statistical literacy and well-informed decisions.

Practice Questions

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

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

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If a square has a perimeter of 64 cm, what is its area?

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

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If 8x = 512, what is the value of x?

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

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