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 new set of values

Options

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

Answer

To solve the problem step by step, we need to follow these calculations:

### Step 1: Identify the given values
- The initial mean (μ) of the set of values is 5.
- The initial standard deviation (σ) of the set of values is 2.

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

### Step 3: Determine the new standard deviation
The standard deviation does not change when a constant is added to each value. Therefore, the new standard deviation (σ') remains the same as the original:
\[ \text{New Standard Deviation} = \text{Old Standard Deviation} = 2 \]

### 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 values:
\[ \text{CV} = \left( \frac{2}{10} \right) \times 100 = 20 \]

### Final Answer
The coefficient of variation for the new set of values is **20**.

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