Two teams A and B have the same mean and their coefficients of variance are 4, 2 respectively. If `sigma_(A), sigma_(B)` are the standard deviations of teams A, B respectively then the relation between item is

Options

A. `sigma_(A) = sigma_(B)`
B. `sigma_(B) = sigma_(2A)`
C. `sigma_(A) = 2sigma_(B)`
D. `sigma_(B) = 4sigma_(A)`

Answer

To solve the problem, we need to analyze the relationship between the standard deviations of teams A and B based on their coefficients of variation.

### Step-by-Step Solution:

1. **Understanding Coefficient of Variation (Cv)**:
The coefficient of variation (Cv) is defined as the ratio of the standard deviation (σ) to the mean (μ), expressed as a percentage:
\[ Cv = \frac{\sigma}{\mu} \times 100 \]
Since both teams A and B have the same mean (μ), we can relate their standard deviations directly through their coefficients of variation.

2. **Setting Up the Relation**:
Let \( Cv_A = 4 \) and \( Cv_B = 2 \). We can express the standard deviations in terms of the coefficients of variation:
\[ Cv_A = \frac{\sigma_A}{\mu} \times 100 \quad \text{and} \quad Cv_B = \frac{\sigma_B}{\mu} \times 100 \]

3. **Expressing Standard Deviations**:
Rearranging the equations for standard deviations, we have:
\[ \sigma_A = \frac{Cv_A \cdot \mu}{100} \quad \text{and} \quad \sigma_B = \frac{Cv_B \cdot \mu}{100} \]

4. **Substituting the Values**:
Now substituting the values of \( Cv_A \) and \( Cv_B \):
\[ \sigma_A = \frac{4 \cdot \mu}{100} = \frac{4\mu}{100} = \frac{\mu}{25} \]
\[ \sigma_B = \frac{2 \cdot \mu}{100} = \frac{2\mu}{100} = \frac{\mu}{50} \]

5. **Finding the Relation Between σ_A and σ_B**:
Now, we can find the relationship between \( \sigma_A \) and \( \sigma_B \):
\[ \frac{\sigma_A}{\sigma_B} = \frac{\frac{4\mu}{100}}{\frac{2\mu}{100}} = \frac{4}{2} = 2 \]
This implies:
\[ \sigma_A = 2 \sigma_B \]

6. **Conclusion**:
Therefore, the relationship between the standard deviations of teams A and B is:
\[ \sigma_A = 2 \sigma_B \]

### Final Answer:
The correct relation is \( \sigma_A = 2 \sigma_B \).