When a data set is multi-modal, the mode(s) is no longer a viable measure of what?

In a multi-modal data set, there are multiple modes, meaning there are multiple values that appear with the highest frequency. While the mode can still provide information about the data set, it becomes less effective as a measure of central tendency. This is because central tendency aims to identify a single representative value that captures the essence of the data distribution.

When a data set is multi-modal, it indicates that the data may have several peaks or clusters, which can obscure a clear central point. As a result, using just the mode to represent the center of the data is insufficient because it doesn't convey which of the modes is the most representative or typical value of the entire set. Instead, other measures of central tendency, such as the mean or median, might provide a more accurate representation of where the center lies, especially in a dataset exhibiting multiple modes.

In contrast, measures such as variability, variance, or sample error can still be calculated and provide valuable insights into aspects of the data regardless of the mode's reliability as a measure of central tendency.