The coefficient of variation of two distribution are 60 and 70 and their standard deviations are 21 and 16 respectively. Find their arithmeticmeans.

Answer

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

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

### Step 2: Set Up the Equation for the First Distribution
For the first distribution:
- Coefficient of Variation (Cv) = 60
- Standard Deviation (SD) = 21

Using the formula:
\[ 60 = \frac{21}{Mean_1} \times 100 \]

### Step 3: Solve for Mean of the First Distribution
Rearranging the equation to solve for Mean_1:
\[ Mean_1 = \frac{21 \times 100}{60} \]
Calculating:
\[ Mean_1 = \frac{2100}{60} = 35 \]

### Step 4: Set Up the Equation for the Second Distribution
For the second distribution:
- Coefficient of Variation (Cv) = 70
- Standard Deviation (SD) = 16

Using the formula:
\[ 70 = \frac{16}{Mean_2} \times 100 \]

### Step 5: Solve for Mean of the Second Distribution
Rearranging the equation to solve for Mean_2:
\[ Mean_2 = \frac{16 \times 100}{70} \]
Calculating:
\[ Mean_2 = \frac{1600}{70} \approx 22.857 \]

### Final Answers
Thus, the arithmetic means for the two distributions are:
- Mean of the first distribution = 35
- Mean of the second distribution ≈ 22.857

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