What is the difference between mean, median and mode, and when is each appropriate?

• Mean — the arithmetic average. Uses every value, which makes it efficient but highly sensitive to outliers.
• Median — the middle value when sorted. Robust to outliers, because moving the largest value further out does not change it.
• Mode — the most frequent value. The only one usable for categorical data.

When to use each:

• Use the mean for roughly symmetric distributions without extreme values, and when you need the total to be recoverable — mean × count gives the sum, which matters for revenue.
• Use the median for skewed distributions. Income, house prices, session duration, and order values are all right-skewed, and the mean overstates the typical case. Median salary and mean salary can differ enormously in the same organisation, which is exactly why the choice matters.
• Use the mode for categories — the most common product, region, or plan.

The relationship tells you about shape: in a symmetric distribution all three roughly coincide. Mean above median indicates right skew; mean below median indicates left skew.

Note: The strongest point is that reporting a central value alone is usually insufficient. Two datasets with identical means can be completely different, so pairing it with a spread measure — standard deviation, IQR, or percentiles — is what makes the summary honest. For latency and response time, percentiles matter far more than the average, because the average hides the worst experiences.