Question

If coefficient of variation is 100, the mean of the data is 25, the standard deviation

• A. 20
• B. 25
• C. 5
• D. 10

Hint:

A coefficient of variation ($CV$) of $100\%$ means that the standard deviation is exactly equal to the mean. This allows you to find the standard deviation instantly without calculation.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The coefficient of variation ($CV$) is a relative measure of dispersion.
It expresses the standard deviation as a percentage of the mean, allowing for comparisons of variability between different datasets regardless of their units or scales.
Key Formula or Approach:
The formula for the coefficient of variation ($CV$) is: \[ CV = \frac{\sigma}{\mu} \times 100 \] where: - $\sigma$ is the standard deviation.
- $\mu$ is the mean of the data.

Step 2: Detailed Explanation:
Let us plug the given values into the equation:
- Coefficient of Variation ($CV$) $= 100$
- Mean ($\mu$) $= 25$
Substitute these values to solve for the standard deviation ($\sigma$): \[ 100 = \frac{\sigma}{25} \times 100 \] Divide both sides by $100$: \[ 1 = \frac{\sigma}{25} \] Multiply both sides by $25$: \[ \sigma = 25 \] Therefore, the standard deviation of the data is $25$.

Step 3: Final Answer:
The standard deviation of the data is $25$.
Hence, the correct option is (B).