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The arithmetic mean and coffecient of variable of data set Xare respectively , 10and 30 . the variance pf 30 - 2X is?
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The arithmetic mean and coffecient of variable of data set Xare respec...
Understanding the Problem
To find the variance of the transformed data set 30 - 2X, we first need to understand the properties of the variance and how transformations affect it.
Given Information
- Arithmetic Mean of X = 10
- Coefficient of Variation of X = 30
Coefficient of Variation Explained
- The Coefficient of Variation (CV) is defined as the ratio of the standard deviation to the mean, expressed as a percentage.
- Therefore, the standard deviation (σ) can be calculated using the CV:
CV = (σ / Mean) * 100
- Rearranging gives: σ = (CV / 100) * Mean = (30 / 100) * 10 = 3
Calculating Variance of X
- Variance (Var(X)) is the square of the standard deviation:
Var(X) = σ² = 3² = 9
Transformation of the Data Set
When transforming a data set, the variance is affected as follows:
1. Linear Transformations:
- If Y = a + bX, then Var(Y) = b² * Var(X)
- Here, a = 30 and b = -2.
2. Applying the Transformation:
- So, we have:
Var(30 - 2X) = (-2)² * Var(X)
Calculating the Variance
- Substituting the variance of X:
Var(30 - 2X) = 4 * 9 = 36
Conclusion
The variance of the data set 30 - 2X is 36. This transformation shows how scaling affects the spread of the data, while shifting does not alter the variance.
To find the variance of the transformed data set 30 - 2X, we first need to understand the properties of the variance and how transformations affect it.
Given Information
- Arithmetic Mean of X = 10
- Coefficient of Variation of X = 30
Coefficient of Variation Explained
- The Coefficient of Variation (CV) is defined as the ratio of the standard deviation to the mean, expressed as a percentage.
- Therefore, the standard deviation (σ) can be calculated using the CV:
CV = (σ / Mean) * 100
- Rearranging gives: σ = (CV / 100) * Mean = (30 / 100) * 10 = 3
Calculating Variance of X
- Variance (Var(X)) is the square of the standard deviation:
Var(X) = σ² = 3² = 9
Transformation of the Data Set
When transforming a data set, the variance is affected as follows:
1. Linear Transformations:
- If Y = a + bX, then Var(Y) = b² * Var(X)
- Here, a = 30 and b = -2.
2. Applying the Transformation:
- So, we have:
Var(30 - 2X) = (-2)² * Var(X)
Calculating the Variance
- Substituting the variance of X:
Var(30 - 2X) = 4 * 9 = 36
Conclusion
The variance of the data set 30 - 2X is 36. This transformation shows how scaling affects the spread of the data, while shifting does not alter the variance.
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The arithmetic mean and coffecient of variable of data set Xare respectively , 10and 30 . the variance pf 30 - 2X is? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The arithmetic mean and coffecient of variable of data set Xare respectively , 10and 30 . the variance pf 30 - 2X is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The arithmetic mean and coffecient of variable of data set Xare respectively , 10and 30 . the variance pf 30 - 2X is?.
The arithmetic mean and coffecient of variable of data set Xare respectively , 10and 30 . the variance pf 30 - 2X is? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The arithmetic mean and coffecient of variable of data set Xare respectively , 10and 30 . the variance pf 30 - 2X is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The arithmetic mean and coffecient of variable of data set Xare respectively , 10and 30 . the variance pf 30 - 2X is?.
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