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What is the coefficient of variation for the following distribution of wages Delhi 30 40 40 50 50 number of 1728 2115 13?
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What is the coefficient of variation for the following distribution of...
Calculation of Coefficient of Variation
1. Calculate the Mean:
- Mean = Σ (wages * number of employees) / Total number of employees
- Mean = (30*1728 + 40*2115 + 50*13) / (1728 + 2115 + 13)
- Mean = (51840 + 84600 + 650) / 3856
- Mean = 137090 / 3856
- Mean = 35.53
2. Calculate the Standard Deviation:
- Standard Deviation = √[Σ((wages - mean)^2 * number of employees) / Total number of employees]
- Standard Deviation = √[(1728*(30-35.53)^2 + 2115*(40-35.53)^2 + 13*(50-35.53)^2) / 3856]
- Standard Deviation = √[(1728*30.53^2 + 2115*4.47^2 + 13*14.47^2) / 3856]
- Standard Deviation = √[(1728*930.64 + 2115*19.99 + 13*209.60) / 3856]
- Standard Deviation = √(1610070.72 + 42351.85 + 2985.80) / 3856
- Standard Deviation = √1656408.37 / 3856
- Standard Deviation = √429.26
- Standard Deviation ≈ 20.71
3. Calculate the Coefficient of Variation:
- Coefficient of Variation = (Standard Deviation / Mean) * 100
- Coefficient of Variation = (20.71 / 35.53) * 100
- Coefficient of Variation ≈ 58.26%
Conclusion:
The coefficient of variation for the distribution of wages in Delhi is approximately 58.26%. This indicates a moderate level of variability relative to the mean wage.
1. Calculate the Mean:
- Mean = Σ (wages * number of employees) / Total number of employees
- Mean = (30*1728 + 40*2115 + 50*13) / (1728 + 2115 + 13)
- Mean = (51840 + 84600 + 650) / 3856
- Mean = 137090 / 3856
- Mean = 35.53
2. Calculate the Standard Deviation:
- Standard Deviation = √[Σ((wages - mean)^2 * number of employees) / Total number of employees]
- Standard Deviation = √[(1728*(30-35.53)^2 + 2115*(40-35.53)^2 + 13*(50-35.53)^2) / 3856]
- Standard Deviation = √[(1728*30.53^2 + 2115*4.47^2 + 13*14.47^2) / 3856]
- Standard Deviation = √[(1728*930.64 + 2115*19.99 + 13*209.60) / 3856]
- Standard Deviation = √(1610070.72 + 42351.85 + 2985.80) / 3856
- Standard Deviation = √1656408.37 / 3856
- Standard Deviation = √429.26
- Standard Deviation ≈ 20.71
3. Calculate the Coefficient of Variation:
- Coefficient of Variation = (Standard Deviation / Mean) * 100
- Coefficient of Variation = (20.71 / 35.53) * 100
- Coefficient of Variation ≈ 58.26%
Conclusion:
The coefficient of variation for the distribution of wages in Delhi is approximately 58.26%. This indicates a moderate level of variability relative to the mean wage.
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What is the coefficient of variation for the following distribution of wages Delhi 30 40 40 50 50 number of 1728 2115 13?
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What is the coefficient of variation for the following distribution of wages Delhi 30 40 40 50 50 number of 1728 2115 13? 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 What is the coefficient of variation for the following distribution of wages Delhi 30 40 40 50 50 number of 1728 2115 13? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the coefficient of variation for the following distribution of wages Delhi 30 40 40 50 50 number of 1728 2115 13?.
What is the coefficient of variation for the following distribution of wages Delhi 30 40 40 50 50 number of 1728 2115 13? 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 What is the coefficient of variation for the following distribution of wages Delhi 30 40 40 50 50 number of 1728 2115 13? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the coefficient of variation for the following distribution of wages Delhi 30 40 40 50 50 number of 1728 2115 13?.
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