If the coefficient of variation of a distribution is 60 and its is s.d. is 21, then find its arithmetic mean

Answer

To find the arithmetic mean given the coefficient of variation and the standard deviation, we can follow these steps:

### Step 1: Understand the formula for Coefficient of Variation (CV)
The Coefficient of Variation (CV) is defined as:
\[ CV = \frac{\sigma}{\bar{x}} \times 100 \]
where:
- \( \sigma \) is the standard deviation,
- \( \bar{x} \) is the arithmetic mean.

### Step 2: Substitute the known values into the formula
We are given:
- \( CV = 60 \)
- \( \sigma = 21 \)

Substituting these values into the formula:
\[ 60 = \frac{21}{\bar{x}} \times 100 \]

### Step 3: Rearrange the equation to solve for \( \bar{x} \)
To isolate \( \bar{x} \), we can rearrange the equation:
\[ \bar{x} = \frac{21 \times 100}{60} \]

### Step 4: Calculate \( \bar{x} \)
Now, we can perform the calculation:
\[ \bar{x} = \frac{2100}{60} = 35 \]

### Step 5: Conclusion
Thus, the arithmetic mean \( \bar{x} \) is:
\[ \bar{x} = 35 \]