📊 Statistics Calculator
Compute mean, median, mode, standard deviation and more.
What is this tool?
The Statistics Calculator is a free online tool that computes a comprehensive set of descriptive statistics from any data set. Whether you are analyzing survey results, scientific data, or business metrics, this calculator provides all the key statistical measures in one place with instant results. Statistics help us summarize and understand data. The most basic measures describe the center of the data: the mean (average), median (middle value), and mode (most frequent value). Measures of spread tell us how dispersed the data is: range (difference between max and min), variance, and standard deviation. Position measures like quartiles and percentiles show where individual data points fall within the distribution. This calculator handles all of these measures plus more advanced statistics like skewness (asymmetry of the distribution) and kurtosis (how heavy the tails are). It supports both population and sample statistics, since the formulas differ slightly depending on whether your data represents the entire population or just a sample. Simply enter your numbers separated by commas, spaces, or new lines, and get a complete statistical summary instantly. All calculations happen locally in your browser.How it works
The calculator computes each statistic using standard formulas. The arithmetic mean is the sum of all values divided by the count: x̄ = (Σxᵢ) / n. The median is found by sorting the data and taking the middle value (or the average of the two middle values if the count is even). The mode is the most frequently occurring value, and there can be multiple modes or none. Variance measures the average squared deviation from the mean. For a population: σ² = Σ(xᵢ - x̄)² / n. For a sample: s² = Σ(xᵢ - x̄)² / (n - 1). The sample formula uses n-1 (Bessel's correction) to provide an unbiased estimate of the population variance. Standard deviation is simply the square root of variance, bringing the measure back to the same units as the original data. Quartiles divide the sorted data into four equal parts: Q1 (25th percentile), Q2 (median, 50th percentile), and Q3 (75th percentile). The interquartile range (IQR = Q3 - Q1) measures the spread of the middle 50% of data and is resistant to outliers. Skewness measures the asymmetry of the distribution, and kurtosis measures the heaviness of tails compared to a normal distribution.How to use
- Enter your data set (comma or space separated).
- Choose population or sample statistics.
- Click Calculate to compute all measures.
- Review mean, median, mode, and spread measures.
- Copy the results for your report or analysis.
Frequently Asked Questions
Frequently Asked Questions
What is the difference between mean and median?
The mean is the arithmetic average (sum divided by count). The median is the middle value when data is sorted. The median is less affected by extreme values (outliers), making it better for skewed data like income distributions.
When should I use sample vs population standard deviation?
Use population standard deviation when your data includes every member of the population. Use sample standard deviation (n-1 in the denominator) when your data is a sample from a larger population, to get an unbiased estimate.
What does standard deviation tell me?
Standard deviation measures how spread out the data is around the mean. A low standard deviation means data points are close to the mean; a high standard deviation means they are spread over a wide range. For normal distributions, about 68% of data falls within one standard deviation of the mean.
What is the interquartile range (IQR)?
The IQR is the difference between the third quartile (Q3, 75th percentile) and the first quartile (Q1, 25th percentile). It measures the spread of the middle 50% of data and is resistant to outliers, making it useful for identifying unusual values.
Tips & Advice
Always check whether you need population or sample statistics — the formulas differ by using n vs n-1 in the denominator for variance and standard deviation. The median is more robust than the mean when data has outliers or is heavily skewed (like income or housing prices). The interquartile range (IQR) is an excellent outlier detector: values below Q1 - 1.5×IQR or above Q3 + 1.5×IQR are often flagged as potential outliers. Standard deviation is most meaningful for roughly symmetric, bell-shaped distributions; for skewed data, consider reporting the median and IQR instead. Always look at your data with multiple statistics to get a complete picture.