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If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x?
Most Upvoted Answer
If Arithmetic mean and coefficient of variation of X are 5 and 20 resp...
Solution:
Given, Arithmetic Mean of X = 5
Coefficient of Variation of X = 20%
Let us assume X follows a Normal Distribution.
Step 1: Finding the Standard Deviation of X
Coefficient of Variation (CV) = (Standard Deviation / Arithmetic Mean) × 100
⇒ Standard Deviation of X = CV × Arithmetic Mean / 100
⇒ Standard Deviation of X = 20/100 × 5
⇒ Standard Deviation of X = 1
Step 2: Finding the Mean and Standard Deviation of 15 - 2X
Mean of 15 - 2X = 15 - 2 × Mean of X
⇒ Mean of 15 - 2X = 15 - 2 × 5
⇒ Mean of 15 - 2X = 5
Standard Deviation of 15 - 2X = 2 × Standard Deviation of X
⇒ Standard Deviation of 15 - 2X = 2 × 1
⇒ Standard Deviation of 15 - 2X = 2
Step 3: Finding the Variance of 15 - 2X
Variance of 15 - 2X = (Standard Deviation of 15 - 2X)^2
⇒ Variance of 15 - 2X = 2^2
⇒ Variance of 15 - 2X = 4
Therefore, the Variance of 15 - 2X = 4.
Given, Arithmetic Mean of X = 5
Coefficient of Variation of X = 20%
Let us assume X follows a Normal Distribution.
Step 1: Finding the Standard Deviation of X
Coefficient of Variation (CV) = (Standard Deviation / Arithmetic Mean) × 100
⇒ Standard Deviation of X = CV × Arithmetic Mean / 100
⇒ Standard Deviation of X = 20/100 × 5
⇒ Standard Deviation of X = 1
Step 2: Finding the Mean and Standard Deviation of 15 - 2X
Mean of 15 - 2X = 15 - 2 × Mean of X
⇒ Mean of 15 - 2X = 15 - 2 × 5
⇒ Mean of 15 - 2X = 5
Standard Deviation of 15 - 2X = 2 × Standard Deviation of X
⇒ Standard Deviation of 15 - 2X = 2 × 1
⇒ Standard Deviation of 15 - 2X = 2
Step 3: Finding the Variance of 15 - 2X
Variance of 15 - 2X = (Standard Deviation of 15 - 2X)^2
⇒ Variance of 15 - 2X = 2^2
⇒ Variance of 15 - 2X = 4
Therefore, the Variance of 15 - 2X = 4.
Community Answer
If Arithmetic mean and coefficient of variation of X are 5 and 20 resp...
First find out the sd of X.
See,
Coefficient of variation = SD/Mean*100%
Assuming CoV is given in percentage,
=> SD = Mean*COV = 10*40% = 4
=> Var(X) = 16
Var(15-2X) = 4*Var(X) = 4*16 = 64
Note: If the CoV is not given in percentage please adjust accordingly
See,
Coefficient of variation = SD/Mean*100%
Assuming CoV is given in percentage,
=> SD = Mean*COV = 10*40% = 4
=> Var(X) = 16
Var(15-2X) = 4*Var(X) = 4*16 = 64
Note: If the CoV is not given in percentage please adjust accordingly
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If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x?
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If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? 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 If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x?.
If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? 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 If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If Arithmetic mean and coefficient of variation of X are 5 and 20 respectively what is the variance of 15 - 2x?.
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