What is the difference between mean, median and mode, and when should I use each?

All three are measures of central tendency but capture different things. The mean is the arithmetic average, the sum of all values divided by their count, and it uses every data value, so it is sensitive to extreme values. The median is the middle value when data is arranged in order, so it is unaffected by extremes and is best when the data has outliers, like incomes. The mode is the value that occurs most frequently, useful for finding the most common or popular item, like shoe sizes. For grouped data each has its own formula. As a rule, use mean for balanced data, median when there are outliers, and mode when you want the most frequent observation.