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Statistics Calculator

Calculate mean, median, standard deviation, quartiles and more. Distribution table, box plot and histogram included.

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Enter your dataset and click Calculate.

How to calculate descriptive statistics?

Descriptive statistics summarize and analyze a numerical dataset through key indicators: central tendency (mean, median, mode), dispersion (variance, standard deviation, range) and distribution (quartiles, IQR). This calculator handles series of 2 to 1,000 values.

Mean, median and mode

The arithmetic mean (μ) is the sum of values divided by their count. The median is the central value that splits the ordered series into two equal halves. The mode is the most frequent value. These three indicators characterize the central tendency of a series.

Standard deviation and variance

Variance (σ²) measures the dispersion of values around the mean: σ² = Σ(xᵢ−μ)²/n. Standard deviation (σ) is the square root of variance. The larger σ, the more spread out the data. IQR (interquartile range = Q3−Q1) measures the spread of the central 50%.

Frequently asked questions

Population variance (σ²) divides by n and is used when the series represents the complete population. Sample variance (s²) divides by n−1 (Bessel's correction) ... Population variance (σ²) divides by n and is used when the series represents the complete population. Sample variance (s²) divides by n−1 (Bessel's correction) and is used when the series is a sample of a larger population. For large n, the difference is negligible. In practice, σ² (division by n) is most commonly used in education.

Our calculator uses linear interpolation (inclusive method). Q1 is the value at rank 0.25×(n−1) and Q3 at rank 0.75×(n−1) in the sorted series. If the index is ... Our calculator uses linear interpolation (inclusive method). Q1 is the value at rank 0.25×(n−1) and Q3 at rank 0.75×(n−1) in the sorted series. If the index is not an integer, we linearly interpolate between the two adjacent values. This is the method used by NumPy, Excel (QUARTILE.INC) and most scientific calculators.

Tukey's rule identifies as outliers all values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. IQR (interquartile range) is the difference Q3 − Q1. This rule is r... Tukey's rule identifies as outliers all values below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR. IQR (interquartile range) is the difference Q3 − Q1. This rule is robust and widely used in exploratory data analysis. Outliers are shown in red in the box plot.

Skewness measures the asymmetry of the distribution. A skewness close to 0 indicates a symmetric distribution (close to normal). Positive skewness (right skewed... Skewness measures the asymmetry of the distribution. A skewness close to 0 indicates a symmetric distribution (close to normal). Positive skewness (right skewed) means the tail is longer on the right — most data is concentrated on the left. Negative skewness means the opposite. As a rule of thumb, |skewness| < 0.5 is considered moderately symmetric.

The number of bins is automatically calculated using Sturges' rule: k = 1 + 3.322 × log₁₀(n), with a minimum of 5 and maximum of 20 bins. Each bin has the same ... The number of bins is automatically calculated using Sturges' rule: k = 1 + 3.322 × log₁₀(n), with a minimum of 5 and maximum of 20 bins. Each bin has the same width. The overlaid normal curve is calculated from the series mean and standard deviation, allowing you to visualize how close the distribution is to normal.

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