Statistics Calculator

Key statistical measures

• Mean: the sum of all values divided by their count — the most common measure of central tendency.
• Median: the middle value in a sorted data set. If the count is even, the median is the average of the two middle numbers.
• Mode: the value (or values) that occur most frequently in the data set.
• Standard deviation: a measure of how spread out the data is relative to the mean.
• Variance: the square of the standard deviation, another measure of data spread.
• Range: the difference between the largest and smallest value in the set.

Why median is sometimes better than mean

The mean is sensitive to extreme values (outliers). For example, in a salary set [30000, 32000, 35000, 500000], the mean will be skewed by one very large value and won't reflect a typical salary. In this case, the median gives a more accurate picture of a "typical" value, since it doesn't depend on how far an outlier is from the rest of the data.

How to interpret standard deviation

Standard deviation shows the "typical" distance of values from the mean. A small standard deviation means data is tightly clustered around the mean (low variability). A large standard deviation means a wide spread of values (high variability). This is a key metric in statistics, finance (volatility), and quality control.

Practical applications of statistics

• Education: analyzing test results, comparing grades across a student group.
• Scientific research: describing a data sample before further statistical analysis.
• Business: sales analysis, evaluating metric stability.
• Sports: analyzing player or team performance over a season.

This calculator computes sample standard deviation (dividing by n−1), which is the standard when working with a data sample rather than an entire population.