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The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is
- a)40 %
- b)10 %
- c)50 %
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Given information:
- The sum of the squared deviations for 10 observations taken from their mean 50 is 250.
To find:
The coefficient of variation.
Solution:
The coefficient of variation is a measure of relative variability and is calculated as the standard deviation divided by the mean, expressed as a percentage.
Step 1: Find the standard deviation:
The sum of the squared deviations is given as 250. We have 10 observations, so the formula to calculate the variance is:
Variance = Sum of squared deviations / (Number of observations - 1)
Variance = 250 / (10 - 1)
Variance = 250 / 9
Variance ≈ 27.78
The standard deviation is the square root of the variance:
Standard deviation ≈ √27.78 ≈ 5.27
Step 2: Find the mean:
The mean is given as 50.
Step 3: Calculate the coefficient of variation:
Coefficient of variation = (Standard deviation / Mean) * 100
Coefficient of variation = (5.27 / 50) * 100
Coefficient of variation ≈ 10.54
Answer:
The coefficient of variation is approximately 10.54%. Therefore, the correct option is B) 10%.
- The sum of the squared deviations for 10 observations taken from their mean 50 is 250.
To find:
The coefficient of variation.
Solution:
The coefficient of variation is a measure of relative variability and is calculated as the standard deviation divided by the mean, expressed as a percentage.
Step 1: Find the standard deviation:
The sum of the squared deviations is given as 250. We have 10 observations, so the formula to calculate the variance is:
Variance = Sum of squared deviations / (Number of observations - 1)
Variance = 250 / (10 - 1)
Variance = 250 / 9
Variance ≈ 27.78
The standard deviation is the square root of the variance:
Standard deviation ≈ √27.78 ≈ 5.27
Step 2: Find the mean:
The mean is given as 50.
Step 3: Calculate the coefficient of variation:
Coefficient of variation = (Standard deviation / Mean) * 100
Coefficient of variation = (5.27 / 50) * 100
Coefficient of variation ≈ 10.54
Answer:
The coefficient of variation is approximately 10.54%. Therefore, the correct option is B) 10%.
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The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation isa)40 %b)10 %c)50 %d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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