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If arithmetic mean and coefficient of variation of X are 10 and 40 for respectively then the variance of -15+3x/2?
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If arithmetic mean and coefficient of variation of X are 10 and 40 for...
Understanding the Problem
To find the variance of the transformed variable Y = -15 + (3X/2), we start with the given properties of X:
- Arithmetic Mean of X (μ) = 10
- Coefficient of Variation (CV) = 40
Key Definitions
- Coefficient of Variation (CV): CV is defined as the ratio of the standard deviation (σ) to the mean (μ) and is expressed as a percentage. Given CV = 40, we can say:
- CV = (σ/μ) * 100
- Therefore, σ = (CV/100) * μ = (40/100) * 10 = 4.
- Variance (σ²): Variance is the square of the standard deviation. Thus:
- Variance of X = σ² = 4² = 16.
Transformation of the Variable
For the transformation Y = -15 + (3X/2):
- Mean of Y: The mean of a transformed variable can be calculated as:
- Mean of Y = -15 + (3/2) * μ = -15 + (3/2) * 10 = -15 + 15 = 0.
- Variance of Y: Since variance is affected only by the scaling factor (not the constant), we have:
- Variance of Y = (scaling factor)² * Variance of X.
- Here, the scaling factor is 3/2, so:
- Variance of Y = (3/2)² * 16 = (9/4) * 16 = 36.
Conclusion
The variance of the transformed variable Y = -15 + (3X/2) is 36.
To find the variance of the transformed variable Y = -15 + (3X/2), we start with the given properties of X:
- Arithmetic Mean of X (μ) = 10
- Coefficient of Variation (CV) = 40
Key Definitions
- Coefficient of Variation (CV): CV is defined as the ratio of the standard deviation (σ) to the mean (μ) and is expressed as a percentage. Given CV = 40, we can say:
- CV = (σ/μ) * 100
- Therefore, σ = (CV/100) * μ = (40/100) * 10 = 4.
- Variance (σ²): Variance is the square of the standard deviation. Thus:
- Variance of X = σ² = 4² = 16.
Transformation of the Variable
For the transformation Y = -15 + (3X/2):
- Mean of Y: The mean of a transformed variable can be calculated as:
- Mean of Y = -15 + (3/2) * μ = -15 + (3/2) * 10 = -15 + 15 = 0.
- Variance of Y: Since variance is affected only by the scaling factor (not the constant), we have:
- Variance of Y = (scaling factor)² * Variance of X.
- Here, the scaling factor is 3/2, so:
- Variance of Y = (3/2)² * 16 = (9/4) * 16 = 36.
Conclusion
The variance of the transformed variable Y = -15 + (3X/2) is 36.
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If arithmetic mean and coefficient of variation of X are 10 and 40 for respectively then the variance of -15+3x/2?
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If arithmetic mean and coefficient of variation of X are 10 and 40 for respectively then the variance of -15+3x/2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If arithmetic mean and coefficient of variation of X are 10 and 40 for respectively then the variance of -15+3x/2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If arithmetic mean and coefficient of variation of X are 10 and 40 for respectively then the variance of -15+3x/2?.
If arithmetic mean and coefficient of variation of X are 10 and 40 for respectively then the variance of -15+3x/2? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If arithmetic mean and coefficient of variation of X are 10 and 40 for respectively then the variance of -15+3x/2? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If arithmetic mean and coefficient of variation of X are 10 and 40 for respectively then the variance of -15+3x/2?.
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