Final answer:
Standard deviations are essential for comparing different data sets because they measure how far data points are from the mean. This allows for accurate comparisons and understanding of data variability in the same units as the data, unlike percentiles, which are less informative in smaller populations or individual comparisons.
Step-by-step explanation:
Understanding the Use of Standard Deviation in Data Comparison
When comparing different groups of variables, standard deviations are preferred over percentiles because they provide a numerical measure of how far data are spread from the mean. While percentiles may be useful for large populations, standard deviation allows for precise comparisons by reflecting the actual distribution of data. In cases of skewed distributions, using the measures of central tendency like quartiles in conjunction with standard deviation is advised for a more accurate analysis.
Standard deviation helps to understand and compare the overall variability or spread of scores within different sets of data. Unlike variance, which is measured in units squared and may not be intuitive, standard deviation is expressed in the same units as the data itself, providing a clear understanding of variability.
When assessing the similarity of data points within a group or between different groups, z-scores are calculated using the mean and standard deviation. This assists in determining whether a specific data value is close to or far from the group's average, facilitating comparisons even when data sets have different means and standard deviations.