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
a. 0
b. 1
c. 1.5
d. 2.5

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 arithmetic 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 arithmetic mean.

2. **Given Values**:
- For Distribution A:
- \(CV_A = 50\)
- \(\bar{x}_A = 30\)
- For Distribution B:
- \(CV_B = 60\)
- \(\bar{x}_B = 25\)

3. **Setting Up the Equations**:
From the definition of CV, we can set up the following equations:
\[ CV_A = \frac{\sigma_A}{\bar{x}_A} \times 100 \implies 50 = \frac{\sigma_A}{30} \times 100 \]
\[ CV_B = \frac{\sigma_B}{\bar{x}_B} \times 100 \implies 60 = \frac{\sigma_B}{25} \times 100 \]

4. **Solving for \(\sigma_A\)**:
Rearranging the equation for Distribution A:
\[ 50 = \frac{\sigma_A}{30} \times 100 \implies \sigma_A = \frac{50 \times 30}{100} = 15 \]

5. **Solving for \(\sigma_B\)**:
Rearranging the equation for Distribution B:
\[ 60 = \frac{\sigma_B}{25} \times 100 \implies \sigma_B = \frac{60 \times 25}{100} = 15 \]

6. **Finding the Difference**:
Now we find the difference between the standard deviations:
\[ \sigma_A - \sigma_B = 15 - 15 = 0 \]

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

### Final Answer:
The difference of their standard deviations is \(0\). Therefore, the correct option is **a. 0**.

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