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The sum of the squares of deviation of 10 observations from their mean 50 is 250,then coefficient of variation is
Correct answer is '10'. Can you explain this answer?
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Understanding the Problem
In this problem, we have 10 observations with a mean of 50. The sum of the squares of deviations from the mean is given as 250. We need to find the coefficient of variation.
Key Concepts
- Deviation from Mean: The difference between each observation and the mean.
- Sum of Squares of Deviations: This is calculated as \( \sum (x_i - \bar{x})^2 \).
- Variance: It is the average of the sum of squares of deviations, calculated as \( \text{Variance} = \frac{\text{Sum of Squares}}{N} \).
- Standard Deviation: It is the square root of variance.
- Coefficient of Variation (CV): It is the ratio of standard deviation to the mean expressed as a percentage, calculated as \( CV = \left( \frac{\sigma}{\mu} \right) \times 100 \).
Calculating Variance and Standard Deviation
- Given:
- Number of observations (N) = 10
- Mean (\(\mu\)) = 50
- Sum of squares of deviations = 250
- Variance Calculation:
- \( \text{Variance} = \frac{250}{10} = 25 \)
- Standard Deviation Calculation:
- \( \sigma = \sqrt{25} = 5 \)
Calculating Coefficient of Variation
- Coefficient of Variation (CV):
- \( CV = \left( \frac{\sigma}{\mu} \right) \times 100 \)
- \( CV = \left( \frac{5}{50} \right) \times 100 = 10\% \)
Conclusion
The coefficient of variation for the given observations is 10%. This indicates a moderate level of dispersion relative to the mean.
In this problem, we have 10 observations with a mean of 50. The sum of the squares of deviations from the mean is given as 250. We need to find the coefficient of variation.
Key Concepts
- Deviation from Mean: The difference between each observation and the mean.
- Sum of Squares of Deviations: This is calculated as \( \sum (x_i - \bar{x})^2 \).
- Variance: It is the average of the sum of squares of deviations, calculated as \( \text{Variance} = \frac{\text{Sum of Squares}}{N} \).
- Standard Deviation: It is the square root of variance.
- Coefficient of Variation (CV): It is the ratio of standard deviation to the mean expressed as a percentage, calculated as \( CV = \left( \frac{\sigma}{\mu} \right) \times 100 \).
Calculating Variance and Standard Deviation
- Given:
- Number of observations (N) = 10
- Mean (\(\mu\)) = 50
- Sum of squares of deviations = 250
- Variance Calculation:
- \( \text{Variance} = \frac{250}{10} = 25 \)
- Standard Deviation Calculation:
- \( \sigma = \sqrt{25} = 5 \)
Calculating Coefficient of Variation
- Coefficient of Variation (CV):
- \( CV = \left( \frac{\sigma}{\mu} \right) \times 100 \)
- \( CV = \left( \frac{5}{50} \right) \times 100 = 10\% \)
Conclusion
The coefficient of variation for the given observations is 10%. This indicates a moderate level of dispersion relative to the mean.
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The sum of the squares of deviation of 10 observations from their mean 50 is 250,then coefficient of variation isCorrect answer is '10'. Can you explain this answer?
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The sum of the squares of deviation of 10 observations from their mean 50 is 250,then coefficient of variation isCorrect answer is '10'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The sum of the squares of deviation of 10 observations from their mean 50 is 250,then coefficient of variation isCorrect answer is '10'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the squares of deviation of 10 observations from their mean 50 is 250,then coefficient of variation isCorrect answer is '10'. Can you explain this answer?.
The sum of the squares of deviation of 10 observations from their mean 50 is 250,then coefficient of variation isCorrect answer is '10'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about The sum of the squares of deviation of 10 observations from their mean 50 is 250,then coefficient of variation isCorrect answer is '10'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the squares of deviation of 10 observations from their mean 50 is 250,then coefficient of variation isCorrect answer is '10'. Can you explain this answer?.
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