The mean is calculated by adding up all the numbers in the data set and dividing by the number of values in that set. It provides a measure of the overall trend in the data, but can be skewed by extremely high or low values. The median is the middle value in a data set when the numbers are arranged in ascending or descending order. It is not affected by extreme values, making it a better measure of central tendency when there are outliers in the data. The mode is the value that appears most frequently in a data set. It can be useful in certain situations, particularly with categorical or nominal data where the mean and median cannot be calculated.

The mean is useful for data without outliers but is sensitive to extreme values. The median is robust to outliers and skewed data, while the mode is useful for identifying common values in categorical or discrete data but can be less informative in continuous datasets or if no value repeats. Choosing the right measure depends on the data's nature and the analysis objectives.