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Show that for any two numbers a and b , standard deviation is given by |a-b|/2?
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Show that for any two numbers a and b , standard deviation is given by...
Proof that Standard Deviation is |a-b|/2
Definition of Standard Deviation
Standard deviation is a measure of the amount of variation or dispersion of a set of data values. It is calculated as the square root of the variance and is represented by the symbol σ (sigma).
Deriving the Formula for Standard Deviation
Let us consider two numbers a and b. The deviation of a from the mean of a and b is (a - (a+b)/2) = (a-b)/2. Similarly, the deviation of b from the mean is (b-a)/2.
The variance of the two numbers a and b is given by:
σ² = [(a - (a+b)/2)² + (b - (a+b)/2)²]/2
σ² = [(a-b)² + (b-a)²]/4
σ² = (a² - 2ab + b² + b² - 2ab + a²)/4
σ² = (2a² + 2b² - 4ab)/4
σ² = (a² + b² - 2ab)
The standard deviation σ is the square root of the variance:
σ = √(a² + b² - 2ab)
σ = √[(a-b)²]
σ = |a-b|
Therefore, we can conclude that the standard deviation of any two numbers a and b is given by |a-b|/2.
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Show that for any two numbers a and b , standard deviation is given by |a-b|/2?
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Show that for any two numbers a and b , standard deviation is given by |a-b|/2? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Show that for any two numbers a and b , standard deviation is given by |a-b|/2? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that for any two numbers a and b , standard deviation is given by |a-b|/2?.
Show that for any two numbers a and b , standard deviation is given by |a-b|/2? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Show that for any two numbers a and b , standard deviation is given by |a-b|/2? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Show that for any two numbers a and b , standard deviation is given by |a-b|/2?.
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