Question

The variation in data is compared with another data set by:

• A. Variance
• B. Coefficient of variation
• C. The standard error of mean
• D. Standard deviation

Answer 1

The Correct Option is B

The comparison of variation in data sets typically involves calculating the relative variability rather than the absolute variability. Among the given options, the Coefficient of Variation (CV) is the appropriate measure for this task. The CV is calculated by dividing the standard deviation by the mean of the data set, then multiplying by 100 to express it as a percentage. This normalizes the measure of dispersion relative to the mean, allowing comparison across different datasets regardless of their units or scale.

Here is a concise explanation of why CV is used for comparing data variations:

• The Variance provides the squared deviation from the mean, but its units are the square of the dataset's original units, making direct comparisons difficult when dealing with different datasets.
• The Standard Deviation (SD) gives a measure of dispersion in the same units as the data, but it doesn't account for the magnitude of the mean, limiting its utility in relative comparison.
• The Standard Error of the Mean (SEM) quantifies the variation of sample means, not individual data points, and is primarily used in estimating population means from a sample.
• The Coefficient of Variation, expressed as: CV = (Standard Deviation / Mean) × 100%, provides a dimensionless number, making it ideal for comparing variability across datasets with different units or means.

Therefore, for comparing the variation in data between different datasets, the best choice is the Coefficient of Variation.