The coefficient of variation of two distributions are 70 and 75 and their standard deviations are 28 and 27 respectively. The difference of their arithmetic means is

Options

A. 2
B. 3
C. 4
D. 5

Answer

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

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Coefficient of Variation (CV) for the first distribution = 70
- Standard Deviation (σ1) for the first distribution = 28
- Coefficient of Variation (CV) for the second distribution = 75
- Standard Deviation (σ2) for the second distribution = 27

2. **Recall the Formula for Coefficient of Variation**:
The formula for the Coefficient of Variation is:
\[ CV = \frac{\sigma}{\bar{X}} \times 100 \]
where σ is the standard deviation and \(\bar{X}\) is the arithmetic mean.

3. **Calculate the Arithmetic Mean for the First Distribution**:
Using the formula for CV:
\[ 70 = \frac{28}{\bar{X}_1} \times 100 \]
Rearranging this gives:
\[ \bar{X}_1 = \frac{28 \times 100}{70} \]
Simplifying:
\[ \bar{X}_1 = \frac{2800}{70} = 40 \]

4. **Calculate the Arithmetic Mean for the Second Distribution**:
Using the formula for CV:
\[ 75 = \frac{27}{\bar{X}_2} \times 100 \]
Rearranging this gives:
\[ \bar{X}_2 = \frac{27 \times 100}{75} \]
Simplifying:
\[ \bar{X}_2 = \frac{2700}{75} = 36 \]

5. **Find the Difference of the Arithmetic Means**:
Now, we need to find the difference between the two means:
\[ \text{Difference} = \bar{X}_1 - \bar{X}_2 = 40 - 36 = 4 \]

### Final Answer:
The difference of their arithmetic means is **4**.