Question:easy

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

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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.
Updated On: Jun 12, 2026
  • 15.67
  • 14.67
  • 13.67
  • 16.67
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Recall what coefficient of variation measures.
The coefficient of variation (CV) tells us how spread out the data is relative to its average. It lets us compare consistency between two data sets even when their sizes differ.
Step 2: Write the working formula.
$\text{CV} = \dfrac{\sigma}{\bar{x}} \times 100$, where $\sigma$ is the standard deviation and $\bar{x}$ is the mean.
Step 3: List the given values.
Here $\sigma = 12$ and $\bar{x} = 72$.
Step 4: Substitute the values.
$\text{CV} = \dfrac{12}{72} \times 100$.
Step 5: Simplify the fraction first.
$\dfrac{12}{72} = \dfrac{1}{6}$, so $\text{CV} = \dfrac{100}{6}$.
Step 6: Convert to a decimal.
$\dfrac{100}{6} = 16.6\overline{6}$, which rounds to $16.67$. So the data shows about a $16.67\%$ relative variation.
\[ \boxed{\text{CV} = 16.67} \]
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