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For a set of 100 observation taking assumed mean as 4, the sum of deviations is -11 cm and the sum of squares of these deviations is 257cm. The coefficient of variation is?
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For a set of 100 observation taking assumed mean as 4, the sum of devi...
Given:
Calculating Coefficient of Variation:
Coefficient of Variation (CV) is the ratio of the standard deviation to the mean expressed as a percentage. It is used to measure the variability of a dataset relative to its mean.
The formula for CV is:
CV = (Standard Deviation / Mean) x 100
Calculating Mean:
Mean is calculated using the formula:
Mean (x̄) = Assumed Mean + (∑d/n)
Given A = 4 and ∑d = -11, we get:
x̄ = 4 + (-11/100) = 3.89 cm
Calculating Standard Deviation:
Standard Deviation (σ) is calculated using the formula:
σ = √(∑d²/n) - ( ∑d/n )²
Given ∑d² = 257 and n = 100, we get:
σ = √(257/100) - (-11/100)² = 1.61 cm
Calculating Coefficient of Variation:
Using the values of Mean and Standard Deviation, we can calculate the Coefficient of Variation (CV) as follows:
CV = (Standard Deviation / Mean) x 100
CV = (1.61/3.89) x 100 = 41.41%
Conclusion:
The Coefficient of Variation for the given set of 100 observations is 41.41%. This indicates that the dataset is moderately variable relative to its mean.
- Number of observations (n) = 100
- Assumed mean (A) = 4
- Sum of deviations (∑d) = -11 cm
- Sum of squares of deviations (∑d²) = 257cm
Calculating Coefficient of Variation:
Coefficient of Variation (CV) is the ratio of the standard deviation to the mean expressed as a percentage. It is used to measure the variability of a dataset relative to its mean.
The formula for CV is:
CV = (Standard Deviation / Mean) x 100
Calculating Mean:
Mean is calculated using the formula:
Mean (x̄) = Assumed Mean + (∑d/n)
Given A = 4 and ∑d = -11, we get:
x̄ = 4 + (-11/100) = 3.89 cm
Calculating Standard Deviation:
Standard Deviation (σ) is calculated using the formula:
σ = √(∑d²/n) - ( ∑d/n )²
Given ∑d² = 257 and n = 100, we get:
σ = √(257/100) - (-11/100)² = 1.61 cm
Calculating Coefficient of Variation:
Using the values of Mean and Standard Deviation, we can calculate the Coefficient of Variation (CV) as follows:
CV = (Standard Deviation / Mean) x 100
CV = (1.61/3.89) x 100 = 41.41%
Conclusion:
The Coefficient of Variation for the given set of 100 observations is 41.41%. This indicates that the dataset is moderately variable relative to its mean.
Community Answer
For a set of 100 observation taking assumed mean as 4, the sum of devi...
 41.38
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For a set of 100 observation taking assumed mean as 4, the sum of deviations is -11 cm and the sum of squares of these deviations is 257cm. The coefficient of variation is?
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For a set of 100 observation taking assumed mean as 4, the sum of deviations is -11 cm and the sum of squares of these deviations is 257cm. The coefficient of variation 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 For a set of 100 observation taking assumed mean as 4, the sum of deviations is -11 cm and the sum of squares of these deviations is 257cm. The coefficient of variation is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a set of 100 observation taking assumed mean as 4, the sum of deviations is -11 cm and the sum of squares of these deviations is 257cm. The coefficient of variation is?.
For a set of 100 observation taking assumed mean as 4, the sum of deviations is -11 cm and the sum of squares of these deviations is 257cm. The coefficient of variation 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 For a set of 100 observation taking assumed mean as 4, the sum of deviations is -11 cm and the sum of squares of these deviations is 257cm. The coefficient of variation is? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For a set of 100 observation taking assumed mean as 4, the sum of deviations is -11 cm and the sum of squares of these deviations is 257cm. The coefficient of variation is?.
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