Average & Statistics Calculator

What are Mean, Median, and Mode?

In statistics, mean, median, and mode are the three primary measurements of "central tendency"—they describe the middle or center points of a data set in different ways:

• Mean (Average) is calculated by adding all the values in a set and dividing the sum by the count of elements. It is the most common average type, though it can be heavily affected by extreme outliers.
• Median is the exact middle value in a data set when it is arranged from lowest to highest. If the set has an even number of values, the median is the average of the two middle numbers. The median is highly useful because it is not skewed by extreme outliers (like house prices or salaries).
• Mode is the number that appears most frequently in a set. A data set can have a single mode, multiple modes (multimodal), or no mode at all if every value is unique.

Understanding Standard Deviation and Variance

Standard deviation and variance measure the **dispersion** or spread of your data points—meaning how far apart the numbers are spread from their average.

Variance is the average of the squared differences from the Mean. A high variance means the numbers are widely scattered, while a low variance means they are clustered tightly around the mean.

Standard Deviation (SD) is the square root of the variance. Because variance is expressed in squared units (which can be hard to visualize), standard deviation returns the measurement to the original unit scale.

The difference between **Sample** and **Population** calculations relates to what data you have. Use Population if your set contains every single item in the group (e.g., the test scores of all students in a classroom). Use Sample if your data is a smaller subset taken from a larger group (e.g., surveying 10 students to represent a whole university).