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The mean, or average, is calculated by summing all the values in a dataset and dividing by the number of values. It provides a measure of central tendency that is sensitive to extreme values, which can skew the result. For example, in a dataset of weights, if one package is significantly heavier than the others, it will raise the mean, potentially misrepresenting the typical weight.

The median is the middle value of a dataset when it is ordered from least to greatest. If there is an even number of observations, the median is the average of the two middle numbers. This measure is less affected by outliers and provides a better representation of the center for skewed distributions. For instance, in a dataset of package weights, the median would indicate the weight at which half the packages are lighter and half are heavier.

The mode is the value that appears most frequently in a dataset. A dataset may have one mode (unimodal), more than one mode (bimodal or multimodal), or no mode at all if all values occur with the same frequency. The mode is particularly useful for categorical data where we wish to know which is the most common category. In the context of package weights, the mode would indicate the weight that occurs most often among the packages.