What will be the coefficient of variation for minimum value = 2, maximum value = 12, total = 40, mean = 10 and standard deviation = 5?
Understand the Problem
The question is asking for the coefficient of variation based on given statistical parameters, specifically minimum value, maximum value, total, mean, and standard deviation. To solve it, we will use the formula for coefficient of variation, which is calculated as the standard deviation divided by the mean, multiplied by 100 to express it as a percentage.
Answer
The coefficient of variation is $50\%$.
Answer for screen readers
The coefficient of variation is $50$%.
Steps to Solve
- Identify the formula for the coefficient of variation
The coefficient of variation (CV) is calculated using the formula:
$$ CV = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100 $$
- Substitute the values into the formula
From the problem, we have:
- Standard Deviation = 5
- Mean = 10
Now, substitute these values into the formula:
$$ CV = \left( \frac{5}{10} \right) \times 100 $$
- Perform the division
Calculate the fraction:
$$ \frac{5}{10} = 0.5 $$
- Multiply by 100
Now multiply by 100 to find the percentage:
$$ CV = 0.5 \times 100 = 50 $$
The coefficient of variation is $50$%.
More Information
The coefficient of variation (CV) expresses the extent of variability in relation to the mean of the data set. A CV of 50% indicates moderate variability, and it is commonly used in fields such as finance and quality control to assess the risk or volatility of a dataset.
Tips
- Miscalculating the mean or standard deviation when substituting values. Always double-check these values are correctly derived from your dataset.
- Forgetting to multiply by 100 to express the coefficient of variation as a percentage.
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