Which measure of center is often considered the best representation of a data set without extreme values?

The median is often considered the best representation of a data set, especially when dealing with values that include extreme outliers. To understand why this is the case, it is essential to recognize how the median is determined. The median is the middle value when a data set is organized in ascending or descending order. In cases where there are extreme values (either very high or very low), the median remains unaffected by these extremes because it focuses solely on the middle point of the data set.

For instance, consider a set of numbers that includes a few very large or very small values. While the mean (average) can be heavily influenced by these extreme values, pulling it in one direction or the other, the median will still accurately reflect the center of the data by considering only the position of the numbers rather than their magnitude. This makes the median a robust measure of center and helps provide a clearer picture of the typical value in a data set without being skewed by outliers.

In contrast, the mode, which represents the most frequently occurring value, may not provide a good sense of the center if the data set doesn't have a clear peak or if multiple values share the highest frequency. The range, while informative about the spread of the data, does not provide