Mean and Standard Deviation Calculator

Calculate mean, median, mode, standard deviation, variance, and range for any dataset. Get complete descriptive statistics with sample and population options. Free statistics calculator.

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Descriptive Statistics Calculator

This calculator computes key descriptive statistics for your dataset, including measures of central tendency (mean, median, mode), measures of dispersion (standard deviation, variance, range), and data characteristics (count, sum, min, max). Descriptive statistics summarize the main features of a dataset, providing a foundation for data analysis.

Understanding the Statistics

Mean (Average)

The arithmetic mean is the sum of all values divided by the count. It represents the center of the data in terms of equal distribution but is sensitive to outliers. A single very large or very small value can significantly shift the mean.

Median

The median is the middle value when data is sorted. For even counts, it's the average of the two middle numbers. The median is robust to outliers and better represents typical values in skewed distributions. Compare the mean and median — if they differ significantly, your data may be skewed.

Mode

The mode is the most frequent value(s) in the dataset. A dataset can have one mode (unimodal), multiple modes (multimodal), or no mode if all values appear equally often. Mode is useful for categorical and discrete data.

Standard Deviation

Standard deviation quantifies how spread out the data is from the mean. It's the square root of the variance and is expressed in the same units as the original data. The empirical rule (68-95-99.7 rule) applies to approximately normal distributions.

Frequently Asked Questions

What is the difference between population and sample standard deviation?
Population standard deviation (σ) uses division by N (all data points) and is used when you have the complete dataset. Sample standard deviation (s) uses division by N-1 (Bessel's correction) to correct for bias when estimating the population parameter from a sample. Always use sample standard deviation when working with a subset of data.
What is the mean in statistics?
The mean (arithmetic average) is the sum of all values divided by the number of values. It's the most commonly used measure of central tendency, but it can be affected by outliers. For skewed distributions, the median is often more representative of the typical value.
How do I interpret standard deviation?
Standard deviation measures the spread of data from the mean. A small standard deviation means data points cluster close to the mean. A large standard deviation means data is spread out. For normally distributed data: about 68% of values fall within ±1σ, 95% within ±2σ, and 99.7% within ±3σ of the mean.

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