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Mean, median, and mode are the three most common measures of central tendency in statistics. They each describe the center of a dataset in a different way. The mean is the arithmetic average. The median is the middle value. The mode is the most frequently occurring value. Together, they give a complete picture of a dataset's distribution.
The mean is most useful when data is symmetric and has no extreme outliers. For example, averaging test scores in a class. The median is better when data is skewed or has outliers — such as household income, where a few very high earners can distort the mean. The mode is most useful for categorical data or when you want to know the most common value — such as the most popular shoe size sold in a store.
Standard deviation measures how spread out values are from the mean. A low standard deviation means values are close to the mean. A high standard deviation means values are more spread out. It is the square root of variance.
Yes. If every value appears exactly once, there is no mode. If two or more values appear the same number of times and more than once, the dataset is bimodal or multimodal.
Population standard deviation (σ) divides by n and is used when you have data for an entire population. Sample standard deviation (s) divides by n−1 and is used when your data is a sample from a larger population. This calculator shows both.