Mean, median, mode, and spread
Descriptive statistics summarize a group of values in different ways. The mean is the arithmetic average; the median is the middle value after sorting; the mode is the most frequently occurring value; and the range is the maximum minus the minimum. Each describes a different feature of a data set.
Worked example
For the values 2, 3, 3, and 7, the mean is (2 + 3 + 3 + 7) ÷ 4 = 3.75, the median is (3 + 3) ÷ 2 = 3, the mode is 3, and the range is 7 − 2 = 5.
The mean can be strongly affected by an unusually high or low value, while the median is often less sensitive to outliers. Standard deviation and variance describe spread, but population and sample formulas use different denominators. Check which definition your class or analysis requires before using those fields.
Tips for accurate results
Enter your data as a list of numbers. The mean is the sum divided by the count, the median is the middle value when sorted, and the mode is the most frequent. For 2, 3, 3, 5, 7, the mean is 4, the median is 3, and the mode is 3.
Common mistakes and limits
Choose between sample and population standard deviation correctly: use the sample version, which divides by n − 1, when your data is a subset of a larger group. A few extreme values can distort the mean, so look at the median too. Statistics describe data and do not by themselves show cause and effect.