If a distribution is not symmetrical, which measure of central tendency is sensitive to outliers and skew-ness?

The mean is the measure of central tendency that is sensitive to outliers and skewness in a distribution. This sensitivity arises because the mean is calculated by summing all values and dividing by the number of observations. Therefore, if there are extreme values (outliers) or if the distribution is skewed (where one tail is longer or thicker than the other), these factors can significantly affect the value of the mean. In a skewed distribution, the mean will often be pulled in the direction of the skew, making it a less reliable indicator of central tendency compared to other measures.

In contrast, the median, which represents the middle value when the data is ordered, is less affected by outliers and provides a better central value for skewed distributions. The mode, being the most frequently occurring value, is also robust to extreme values, as it focuses on frequency rather than the values themselves. The maximum value simply represents the highest point in the dataset and does not convey central tendency.

Understanding the characteristics of these measures helps in choosing the most appropriate one based on the nature of the data. In cases of skewed distributions or the presence of outliers, utilizing the median or mode can often provide a clearer picture of the central tendency than the mean.