Question

If the standard deviation of data is 12 and mean is 72, then coefficient of variation is

• A. 15.67
• B. 14.67
• C. 13.67
• D. 16.67

Hint:

Recognizing common fraction-to-decimal conversions speeds up execution! Remembering that $\frac{1}{6}$ is equal to $0.1666\dots$ allows you to jump directly to $16.67\%$ in your head without performing any long division on paper.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem provides the standard deviation ($\sigma$) and mean ($\bar{x}$) of a data distribution set. We need to calculate its coefficient of variation (CV) expressed as a percentage.

Step 2: Key Formula or Approach:
The coefficient of variation (CV) is a relative measure of data dispersion and is defined as the ratio of the standard deviation to the arithmetic mean, multiplied by 100:
$$\text{CV} = \frac{\text{Standard Deviation }(\sigma)}{\text{Mean }(\bar{x})} \times 100\%$$

Step 3: Detailed Explanation:
Let's plug the given parameters from the problem text directly into our formula:
Standard deviation, $\sigma = 12$
Mean, $\bar{x} = 72$
$$\text{CV} = \frac{12}{72} \times 100\%$$ Simplify the fraction by dividing the numerator and denominator by 12:
$$\frac{12}{72} = \frac{1}{6}$$ $$\text{CV} = \frac{1}{6} \times 100\% = \frac{100}{6}\%$$ Performing long division:
$$\text{CV} = 16.6666\dots\% \approx 16.67\%$$ This matches option (D).

Step 4: Final Answer:
The coefficient of variation is 16.67