Mean Median Mode Calculator

The mean is the total divided by the count. The median is the middle value when sorted. The mode is the most frequent value. They coincide for symmetric data and diverge sharply for skewed data.

Whenever there are outliers or a long tail. Income is reported as a median because a few very high incomes pull the mean well above what a typical person earns.

Yes — if every value appears once there is no mode at all. It can also have several, which usually means two different populations have been combined.

Average the two middle values after sorting. For 1, 2, 3, 4 the median is 2.5, which is not itself in the dataset.

The distribution has a long right tail pulling the mean up. Below, and the tail is on the left. Equal, and the data is roughly symmetric.

The average of the minimum and maximum. It uses only two values and is extremely sensitive to outliers, which is why it is rarely used as a measure of centre.

A mean where each value carries a weight, such as credits per module in a grade average. Ignoring the weights treats a one-credit module as equal to a ten-credit one.

The nth root of the product of n values, used for rates and ratios. It is the correct average for growth rates — averaging 50% growth and −50% growth arithmetically gives zero, and the truth is a 13.4% loss.

The reciprocal of the average of reciprocals, used for rates over a fixed distance. Driving out at 30 mph and back at 60 gives an average of 40, not 45.

For categorical data it is the only one available — there is no mean shoe colour. It is also what a manufacturer wants to know about sizes, since the most common size is what to stock most of.

Usually that two different populations have been combined. Two peaks in a height distribution generally means men and women measured together rather than a genuinely two-peaked group.

Enormously for the mean, not at all for the median, and not at all for the mode unless the outlier repeats. That difference is the entire reason all three are reported.