The mean and standard deviation of a set of values are 5 and 2 respectively. If 5 is added to each value, then what is the coefficient of variation for the bew set of values?

Options

A. 10
B. 20
C. 40
D. 70

Explanation

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given values
We are given:
- Mean (μ) = 5
- Standard Deviation (σ) = 2

### Step 2: Determine the new mean after adding 5 to each value
When we add a constant value to each observation in a dataset, the mean increases by that constant. Therefore, the new mean (μ') can be calculated as follows:
\[ \text{New Mean} = \text{Old Mean} + \text{Constant} = 5 + 5 = 10 \]

### Step 3: Determine the new standard deviation
The standard deviation remains unchanged when a constant is added to each value. Thus, the new standard deviation (σ') is:
\[ \text{New Standard Deviation} = \text{Old Standard Deviation} = 2 \]

### Step 4: Calculate the coefficient of variation (CV)
The coefficient of variation is calculated using the formula:
\[ \text{Coefficient of Variation (CV)} = \left( \frac{\text{Standard Deviation}}{\text{Mean}} \right) \times 100 \]
Substituting the new mean and standard deviation into the formula:
\[ \text{CV} = \left( \frac{2}{10} \right) \times 100 = 20\% \]

### Conclusion
The coefficient of variation for the new set of values is **20%**.

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