# For the recorded observation, the coefficient of variation is 20 and the variance is 16. The arithmetic mean is:

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For the recorded observation, the coefficient of variation is 20 and the variance is 16. The arithmetic mean is:
1. 18
2. 16
3. 20
4. 14

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Correct Answer - Option 3 : 20

Given:

Coefficient of variation (CV) is 20

Variance is 16

Concept

The coefficient of variation (CV)  is defined as the ratio of the standard deviation  to the mean
CV = $\rm \rm \frac{\sigma }{\mu }$ × 100

Calculation:

Standard deviation (σ) = 4

⇒ CV = $\rm \frac{\sigma }{\mu }$ × 100

⇒ 20 = $\rm \frac{4}{\mu }$ × 100

∴ The arithmetic mean is: 20