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If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?
- a)2025
- b)450
- c)45
- d)4.5
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If the mean of a frequency distribution is 100 and the coefficient of ...
Concept:
Coefficient of variation = Standard Deviation/Mean
Variance = (Standard Deviation)2
Calculation:
Given coefficient of variation = 45% = 0.45
And mean = 100
As Coefficient of variation = Standard Deviation/Mean
0.45 = Standard Deviation/100
Standard Deviation = 100 × 0.45
SD = 45
∴ Variance = 452 = 2025
Most Upvoted Answer
If the mean of a frequency distribution is 100 and the coefficient of ...
To find the value of the variance, we need to first understand what the coefficient of variation represents. The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean and multiplying by 100. It is often expressed as a percentage.
Given that the mean of the frequency distribution is 100 and the coefficient of variation is 45%, we can use this information to find the standard deviation.
Let's assume the standard deviation is represented by 's'.
The coefficient of variation (CV) can be calculated using the formula:
CV = (s / mean) * 100
Substituting the given values:
45% = (s / 100) * 100
Simplifying the equation:
0.45 = s / 100
Cross-multiplying:
s = 0.45 * 100
s = 45
Now that we have the value of the standard deviation, we can find the variance using the formula:
Variance = (standard deviation)^2
Substituting the value of the standard deviation:
Variance = 45^2
Variance = 2025
Therefore, the value of the variance is 2025.
Given that the mean of the frequency distribution is 100 and the coefficient of variation is 45%, we can use this information to find the standard deviation.
Let's assume the standard deviation is represented by 's'.
The coefficient of variation (CV) can be calculated using the formula:
CV = (s / mean) * 100
Substituting the given values:
45% = (s / 100) * 100
Simplifying the equation:
0.45 = s / 100
Cross-multiplying:
s = 0.45 * 100
s = 45
Now that we have the value of the standard deviation, we can find the variance using the formula:
Variance = (standard deviation)^2
Substituting the value of the standard deviation:
Variance = 45^2
Variance = 2025
Therefore, the value of the variance is 2025.
Community Answer
If the mean of a frequency distribution is 100 and the coefficient of ...
Concept:
Coefficient of variation = Standard Deviation/Mean
Variance = (Standard Deviation)2
Calculation:
Given coefficient of variation = 45% = 0.45
And mean = 100
As Coefficient of variation = Standard Deviation/Mean
0.45 = Standard Deviation/100
Standard Deviation = 100 × 0.45
SD = 45
∴ Variance = 452 = 2025
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