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If x and y are related by y = 2x 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation of y is?
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If x and y are related by y = 2x 5 and the SD and AM of x are known t...
Calculation of Coefficient of Variation of y
Given:
- Relationship between x and y: y = 2x - 5
- Standard Deviation (SD) of x: 5
- Arithmetic Mean (AM) of x: 10
Calculating the SD of y:
1. Since y = 2x - 5, we can rewrite it as x = (y + 5)/2
2. We know that SD of x = 5, so SD of y can be calculated as follows:
SD(y) = 2 * SD(x) = 2 * 5 = 10
Calculating the Coefficient of Variation (CV) of y:
1. Coefficient of Variation is calculated as the ratio of SD to AM.
2. CV(y) = (SD(y) / AM(y)) * 100
3. Since AM(y) = 2 * AM(x) - 5 = 2 * 10 - 5 = 15
4. Therefore, CV(y) = (10 / 15) * 100 = 66.67%
Explanation:
- The coefficient of variation is a measure of relative variability and is calculated as the ratio of the standard deviation to the mean.
- In this case, we first calculated the standard deviation of y using the relationship between x and y.
- Then, we used the calculated SD of y and the arithmetic mean of y to find the coefficient of variation of y.
- The coefficient of variation of y gives us a measure of how spread out the values of y are relative to its mean, taking into account the scale of the data.
Given:
- Relationship between x and y: y = 2x - 5
- Standard Deviation (SD) of x: 5
- Arithmetic Mean (AM) of x: 10
Calculating the SD of y:
1. Since y = 2x - 5, we can rewrite it as x = (y + 5)/2
2. We know that SD of x = 5, so SD of y can be calculated as follows:
SD(y) = 2 * SD(x) = 2 * 5 = 10
Calculating the Coefficient of Variation (CV) of y:
1. Coefficient of Variation is calculated as the ratio of SD to AM.
2. CV(y) = (SD(y) / AM(y)) * 100
3. Since AM(y) = 2 * AM(x) - 5 = 2 * 10 - 5 = 15
4. Therefore, CV(y) = (10 / 15) * 100 = 66.67%
Explanation:
- The coefficient of variation is a measure of relative variability and is calculated as the ratio of the standard deviation to the mean.
- In this case, we first calculated the standard deviation of y using the relationship between x and y.
- Then, we used the calculated SD of y and the arithmetic mean of y to find the coefficient of variation of y.
- The coefficient of variation of y gives us a measure of how spread out the values of y are relative to its mean, taking into account the scale of the data.
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If x and y are related by y = 2x 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation of y is?
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If x and y are related by y = 2x 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation of y is? 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 x and y are related by y = 2x 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation of y is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are related by y = 2x 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation of y is?.
If x and y are related by y = 2x 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation of y is? 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 x and y are related by y = 2x 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation of y is? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x and y are related by y = 2x 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation of y is?.
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