Find all four measures of centre and spread for any list of numbers.
The four basic measures of a dataset tell you where its centre lies and how spread out it is. The mean (arithmetic average) adds all values and divides by n — it is sensitive to extreme values. The median is the middle value of the sorted list — it ignores outliers. The mode is the most frequent value; datasets can be multimodal (several equally frequent values) or have no mode at all (when every value appears exactly once). The range is simply the maximum minus the minimum.
Mean
Mean = sum of all values / n
Median
For n odd: the middle element of the sorted list. For n even: the average of the two middle elements.
Range
Range = maximum value − minimum value
Use the mean when data is symmetrically distributed with no extreme outliers (e.g. test scores). Use the median when data is skewed or contains outliers (e.g. incomes, house prices). Report both alongside the standard deviation for a complete picture.
Yes. A dataset with two equally frequent values is bimodal; three or more is multimodal. This calculator lists all modes. When every value appears exactly once the dataset has no mode — this calculator displays 'No mode' rather than forcing an incorrect answer.
The range depends only on the two most extreme values and is therefore very sensitive to a single outlier. For most statistical work, the standard deviation or interquartile range are more robust measures of spread.
For symmetric data they coincide. For right-skewed data (e.g. salaries, where a few people earn a lot) the mean is pulled above the median. For left-skewed data the mean falls below the median. The direction of the gap signals which tail is heavier.