mean
Meaning of mean: The familiar average, dependable when values cluster together and easily dragged off course when a few sit far out.
Definition of mean
The mean is the arithmetic average of a set of numbers, found by adding all the values and dividing by how many there are. It is the most widely reported summary of a group of measurements and is the basis for many statistical tests. Because every value contributes, a small number of extreme results can shift the mean well away from what is typical.
How does it compare with the median and mode?
| Measure | Definition | Affected by extremes |
|---|---|---|
| Mean | Sum divided by count | Strongly |
| Median | The middle value when sorted | Barely |
| Mode | The most frequent value | No |
In a symmetrical spread all three sit close together. When the data are skewed, they separate, and the gap between mean and median is itself a signal that the distribution is lopsided.
When is the median reported instead?
Wherever a few very large values are expected. Hospital length of stay is a standard example: most stays are short, a handful run for months, and the mean lands above almost every actual stay. Income, waiting times and the size of a tumor behave the same way. Survival data are reported as a median for a further reason: the mean cannot be calculated until every participant has an outcome, whereas mean survival time and its median counterpart differ in how they handle those still being followed.
What is reported alongside it?
A mean on its own says nothing about how spread out the values were. Two groups can share a mean while one is tightly clustered and the other scattered widely, and the same average result can therefore describe very different situations. Standard deviation is quoted for this reason, summarizing typical distance from the mean. A confidence interval goes further, giving a range within which the true value is likely to lie given the sample size. Comparing two means without any measure of spread is the most common misuse of the statistic, and a p-value quoted without one leaves the size of the difference unknown.
Also known as
Used in a sentence
The mean blood pressure reading was reported alongside the standard deviation.
Good to know
Skewed data pull the mean away from the typical value, which is why length of stay, waiting time and survival are usually reported as medians instead.