CA Foundation Exam > CA Foundation Questions > Show that for any two numbers a and b , stand...
Start Learning for Free
Show that for any two numbers a and b , standard deviation is given by |a-b|/2?
Most Upvoted Answer
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.
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Top Courses for CA FoundationView all
Show that for any two numbers a and b , standard deviation is given by |a-b|/2?
Question Description
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?.
Solutions for Show that for any two numbers a and b , standard deviation is given by |a-b|/2? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of Show that for any two numbers a and b , standard deviation is given by |a-b|/2? defined & explained in the simplest way possible. Besides giving the explanation of
Show that for any two numbers a and b , standard deviation is given by |a-b|/2?, a detailed solution for Show that for any two numbers a and b , standard deviation is given by |a-b|/2? has been provided alongside types of Show that for any two numbers a and b , standard deviation is given by |a-b|/2? theory, EduRev gives you an
ample number of questions to practice Show that for any two numbers a and b , standard deviation is given by |a-b|/2? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup