Question

If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?

• A. \(2025\)
• B. \(450\)
• C. \(45\)
• D. \(4.5\)

Hint:

For problems involving coefficient of variation: - First use \(CV=\frac{\sigma}{\mu}\times100\) to find standard deviation. - Then use Variance \(=\sigma^2\). - Remember: C.V. is always expressed in percentage.

Answer 1

The Correct Option is A

Concept: The coefficient of variation (C.V.) relates standard deviation and mean: \[ CV=\frac{\sigma}{\mu}\times 100 \] where,

• \( \sigma \) = Standard Deviation
• \( \mu \) = Mean

Also, \[ {Variance} = \sigma^2 \] Using the given mean and coefficient of variation, we first find standard deviation, then calculate variance.
Step 1: Use the formula for coefficient of variation. Given: \[ \mu =100 \] \[ CV=45% \] Using \[ CV=\frac{\sigma}{\mu}\times 100 \] Substituting values: \[ 45=\frac{\sigma}{100}\times 100 \]
Step 2: Find the standard deviation. \[ \sigma=45 \]
Step 3: Calculate the variance. Variance is: \[ \sigma^2=(45)^2 \] \[ =2025 \]