Statistical averages summarize a dataset using representative values such as the mean, median, and mode. They help reduce a list of numbers into a few useful descriptions of what the data looks like.

Different averages answer different questions. The mean shows the overall balance of the data, the median shows the middle point, and the mode shows the most common value.

The mean is the most familiar average, but it can be influenced by unusually large or small values. The median is often better when the dataset has outliers because it stays focused on the middle position.

The mode is useful when you want to know the most common value. Some datasets have no mode, while others are multimodal when several values share the highest frequency.

Mean, median, and mode describe different aspects of a dataset. A large outlier can pull the mean toward it while leaving the median much less affected.

Range uses only the minimum and maximum, so it describes the full span but not how values are distributed inside that span. These summaries are descriptive; none of them alone establishes that a value is statistically unusual.

Order does not change the mean, but it does matter for the median because the values must be sorted before the middle can be found. The mode and range also depend on checking the full list carefully.

That is why the calculator sorts the data where needed and still keeps the original values when calculating the totals.