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Statistics Calculators

Descriptive statistics for any data set: mean, median, mode, variance, standard deviation, quartiles and z-scores.

Key statistics formulas

MeanAM = Σx / n · GM = (Πx)^(1/n) · HM = n / Σ(1/x) · RMS = √(Σx² / n)
MedianOdd n: median = x₍₍ₙ₊₁₎/₂₎ · Even n: median = (x₍ₙ/₂₎ + x₍ₙ/₂₊₁₎) / 2
ModeMode = the value with the highest frequency
RangeRange = max − min
Variances² = Σ(x − x̄)² / (n − 1) · σ² = Σ(x − μ)² / N
Standard Deviations = √(Σ(x − x̄)² / (n − 1))
Z-Scorez = (x − μ) / σ
QuartileQ1 = 25th percentile · Q3 = 75th percentile (linear interpolation)
PercentileP-th percentile at position (n − 1)·P/100 + 1 in sorted data
Interquartile RangeIQR = Q3 − Q1 · fences = Q1 − 1.5·IQR, Q3 + 1.5·IQR

Statistics questions

When should I use the geometric mean?

Use it for growth rates and ratios, such as average investment returns over several years, because those values multiply rather than add.

Why use the median instead of the mean?

The median is not pulled by extreme values. For incomes or house prices, the median gives a better picture of a "typical" value than the mean.

Can a data set have more than one mode?

Yes. If two values tie for the highest frequency the data is bimodal; with more it is multimodal. If every value appears once there is no mode.

Sample or population — which should I use?

Use population when your data includes every member of the group you care about. Use sample (dividing by n − 1, Bessel’s correction) when the data is a subset used to estimate a larger population — the most common case.