Question

If the coefficient of variation and mean of a frequency distribution are 5% and 125 respectively, then the standard deviation is:

• A. 0.625
• B. 6.25
• C. 62.5
• D. 625

Hint:

Remember: Coefficient of Variation (CV) is the ratio of the standard deviation to the mean, expressed as a percentage. Always convert percentage to decimal before calculation.

Answer 1

The Correct Option is B

We are given:
Coefficient of Variation (CV) = $5%$ = $5/100 = 0.05$
Mean $(\barx) = 125$
Formula for coefficient of variation:
\[ CV = \frac\sigma\barx \] where $\sigma$ = standard deviation.
Substituting the given values:
\[ 0.05 = \frac\sigma125 \] Multiplying both sides by $125$:
\[ \sigma = 0.05 \times 125 \] \[ \sigma = 6.25 \] Thus, the standard deviation is $\mathbf6.25$.