Which of the following measures is dimensionless?Standard deviationVarianceMean deviationCoefficient of variation
Question
Which of the following measures is dimensionless?
- Standard deviation
- Variance
- Mean deviation
- Coefficient of variation
Solution
The measure that is dimensionless among the options provided is the Coefficient of Variation.
Here's why:
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Standard Deviation: It has the same units as the data. For example, if your data is in meters, then the standard deviation is also in meters.
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Variance: It is the square of the standard deviation, so its units are the square of the units of the data. For example, if your data is in meters, then the variance is in square meters.
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Mean Deviation: Like standard deviation, it has the same units as the data.
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Coefficient of Variation: It is the ratio of the standard deviation to the mean, so the units cancel out, making it dimensionless. It is often expressed as a percentage.
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