The mean, median, and mode are all called 'averages,' but they measure different things and can produce very different numbers from the same dataset. The mean is the sum of all values divided by the count. The median is the middle value when the data is sorted. The mode is the value that appears most often. For a symmetric, bell-shaped distribution, all three are equal. For skewed or outlier-heavy data, they diverge significantly.
Consider household income in a neighborhood where 99 households earn $50,000 and one earns $5,100,000. The mean income is ($50,000 × 99 + $5,100,000) / 100 = $100,500. The median is $50,000. The mode is $50,000. The mean suggests a typical household earns twice what most actually earn — a misleading picture. This is why income statistics are almost always reported as median income.
When the mean is the right choice
The mean is appropriate when the distribution is roughly symmetric and outliers are either absent or meaningful. If you're averaging the temperatures for a week, or the scores on a test where no student scored unusually, the mean is the most efficient estimator of the center — it uses all the information in the data. The mean is also required as an input for many statistical calculations, including standard deviation and linear regression.
The mean is also correct when you need to know the total implied by the average. If you know the mean order value is $47 and you process 1,000 orders, your total revenue is $47,000. The median doesn't have this property — knowing the median order is $35 tells you nothing directly useful about total revenue.
When median and mode are better
Use the median whenever your data is skewed or contains outliers that don't represent the typical case. Real estate prices, salaries, recovery times, and download sizes are classic examples — a few extreme values pull the mean away from where most of the data actually sits. The median is resistant to outliers because it only depends on the middle value, not the magnitude of extreme values.
Use the mode when you're working with categorical data (which has no natural ordering) or when 'most common' is more meaningful than 'average.' What is the most popular shoe size in a store? What is the most common error code in a log file? Neither mean nor median applies to these questions, but mode does. For continuous numerical data, mode is rarely useful because exact repetitions are uncommon.