In a skewed distribution, which measure is typically affected the most?

In a skewed distribution, the mean is typically affected the most because it is sensitive to extreme values or outliers in the dataset. When data is skewed, whether to the left or right, the presence of values that are significantly higher or lower than the bulk of the data can pull the mean in the direction of the skew.

For example, in a right-skewed distribution (where the tail extends to the right), the mean will be greater than both the median and the mode because the high values increase the average. Conversely, in a left-skewed distribution, the mean will be less than both the median and the mode due to the influence of lower values.

In contrast, the median, being the middle value of a dataset when ordered, remains stable and is less influenced by extreme values. The mode, representing the most frequently occurring value, is also not affected significantly by outliers. The range, which measures the difference between the maximum and minimum values, might change with extreme values but does not convey information about the overall center of the distribution like the mean does. Thus, the mean is the measure most impacted in skewed distributions.