If the coefficient of variation of two distribution are 50 ,60 and their arithmetic means are 30 and 25 respectively then the difference of their standard deviation is

Options

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

Explanation

To find the difference of the standard deviations of two distributions given their coefficients of variation and arithmetic means, we can follow these steps:

### Step 1: Understand the Coefficient of Variation
The coefficient of variation (Cv) is defined as:
\[ Cv = \frac{\sigma}{\mu} \times 100 \]
where \(\sigma\) is the standard deviation and \(\mu\) is the mean.

### Step 2: Set Up the Equations
For the first distribution:
- Coefficient of Variation \(Cv_1 = 50\)
- Mean \( \mu_1 = 30\)

Using the formula:
\[ Cv_1 = \frac{\sigma_1}{\mu_1} \times 100 \]
we can rearrange it to find \(\sigma_1\):
\[ \sigma_1 = \frac{Cv_1 \times \mu_1}{100} = \frac{50 \times 30}{100} \]

For the second distribution:
- Coefficient of Variation \(Cv_2 = 60\)
- Mean \( \mu_2 = 25\)

Using the same formula:
\[ Cv_2 = \frac{\sigma_2}{\mu_2} \times 100 \]
we can rearrange it to find \(\sigma_2\):
\[ \sigma_2 = \frac{Cv_2 \times \mu_2}{100} = \frac{60 \times 25}{100} \]

### Step 3: Calculate \(\sigma_1\) and \(\sigma_2\)
Now we can calculate the values:
\[ \sigma_1 = \frac{50 \times 30}{100} = \frac{1500}{100} = 15 \]
\[ \sigma_2 = \frac{60 \times 25}{100} = \frac{1500}{100} = 15 \]

### Step 4: Find the Difference of Standard Deviations
Now, we can find the difference:
\[ \text{Difference} = \sigma_1 - \sigma_2 = 15 - 15 = 0 \]

### Final Answer
The difference of their standard deviations is:
\[ \boxed{0} \]