What determines numerical measures of center and spread are appropriate for describing a given distribution of quantitative variable?

The choice of numerical measures of center (mean, median) and spread (range, variance, standard deviation, interquartile range) depends on the distribution's shape and characteristics. For symmetric distributions without outliers, the mean and standard deviation are appropriate, while for skewed distributions or those with outliers, the median and interquartile range are more robust choices. Additionally, the presence of outliers can significantly affect the mean and standard deviation, making alternative measures more reliable. Understanding the data's distribution helps ensure that the selected measures accurately represent its central tendency and variability.