why might s be more commonly used than s squared as a measure of variability?
The measure of variability is commonly used to describe the dispersion or spread of a data set. Two commonly used measures of variability are the standard deviation (s) and the variance (s²). However, the standard deviation (s) is usually favored over the variance (s²) for a few reasons:
1. Easier interpretation: The standard deviation (s) is expressed in the same units as the original data, making it easier to interpret in real-world terms. On the other hand, the variance (s²) is expressed in squared units, which can be more challenging to understand in practical terms.
2. Better representation: The standard deviation (s) emphasizes the average amount of dispersion from the mean for individual data points. It gives a more intuitive and immediate understanding of the spread of the data. In contrast, the variance (s²) is derived by squaring the standard deviation, which can magnify the dispersion and make interpretation less straightforward.
3. Consistency with mathematical calculations: The standard deviation (s) is mathematically consistent with other common statistical measures, such as the normal distribution and the calculation of confidence intervals. It aligns well with various statistical techniques and formulas. The variance (s²), although related, requires additional calculations or transformations to be used in different statistical methods effectively.
4. Reduced sensitivity to outliers: Squaring the values in the calculation of variance can amplify the impact of outliers in the data set. Outliers are extreme values that deviate significantly from the rest of the data. The standard deviation (s) is less influenced by outliers, as it only involves taking the square root of the variance.
In summary, the standard deviation (s) is commonly used as a measure of variability because it is easier to interpret, provides a better representation of the spread of the data, aligns well with other statistical measures, and is less influenced by outliers compared to the variance (s²).