Coefficients of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25, respectively. Difference of their standard deviations is

Options

A. 0
B. 1
C. 1.5
D. 2.5

Explanation

To solve the problem, we need to find the difference between the standard deviations of two distributions given their coefficients of variation and means.

### Step-by-Step Solution:

1. **Understanding Coefficient of Variation (CV)**:
The coefficient of variation is defined as:
\[ CV = \frac{\sigma}{\bar{X}} \times 100 \]
where \(\sigma\) is the standard deviation and \(\bar{X}\) is the mean.

2. **Setting Up the Equations**:
For the first distribution:
- Coefficient of Variation \(CV_1 = 50\)
- Mean \(\bar{X}_1 = 30\)

For the second distribution:
- Coefficient of Variation \(CV_2 = 60\)
- Mean \(\bar{X}_2 = 25\)

3. **Finding Standard Deviation for the First Distribution**:
Using the formula for \(CV_1\):
\[ 50 = \frac{\sigma_1}{30} \times 100 \]
Rearranging gives:
\[ \sigma_1 = \frac{50 \times 30}{100} = 15 \]

4. **Finding Standard Deviation for the Second Distribution**:
Using the formula for \(CV_2\):
\[ 60 = \frac{\sigma_2}{25} \times 100 \]
Rearranging gives:
\[ \sigma_2 = \frac{60 \times 25}{100} = 15 \]

5. **Calculating the Difference in Standard Deviations**:
Now, we find the difference between the two standard deviations:
\[ \sigma_2 - \sigma_1 = 15 - 15 = 0 \]

6. **Conclusion**:
The difference of their standard deviations is \(0\).

### Final Answer:
The difference of their standard deviations is \(0\).

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