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| Q. |
If the arithmetic mean is multiplied to coefficient of variation then the resulting value is classified as |
| A. | coefficient of deviation |
| B. | coefficient of mean |
| C. | standard deviation |
| D. | variance |
| Answer» C. standard deviation | |
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SREENIVASA H HALUVADI
3 weeks ago
The resulting value of multiplying the arithmetic mean (µ) by the coefficient of variation (CV) is closely related to the standard deviation (σ) of the data set.
Here's why:
Coefficient of Variation (CV): CV is a unitless measure of relative dispersion. It's calculated as the ratio of the standard deviation (σ) to the mean (µ): CV = σ / µ.
Multiplication: When you multiply the mean (µ) by the CV, you're essentially multiplying the mean by (σ / µ). This simplifies to σ, the standard deviation.
Therefore, multiplying the arithmetic mean by the coefficient of variation results in a value that represents the standard deviation (σ).
Here's why:
Coefficient of Variation (CV): CV is a unitless measure of relative dispersion. It's calculated as the ratio of the standard deviation (σ) to the mean (µ): CV = σ / µ.
Multiplication: When you multiply the mean (µ) by the CV, you're essentially multiplying the mean by (σ / µ). This simplifies to σ, the standard deviation.
Therefore, multiplying the arithmetic mean by the coefficient of variation results in a value that represents the standard deviation (σ).
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