Statistics Calculator

If every value appears exactly once, there is no mode. The calculator returns 'none' (empty list). If multiple values are tied for the highest frequency, all are returned as modes.

Using linear interpolation on the sorted values (the same method as Python's statistics.quantiles). Q1 is the 25th percentile, Q3 is the 75th, and IQR is Q3 − Q1. For small datasets, some textbooks use different rules (Tukey's hinges) — results may differ slightly.

Arithmetic mean is the standard average — useful for additive quantities. Geometric mean (only positive numbers) is the nth root of the product — useful for growth rates, ratios, and compound returns. Harmonic mean is n divided by the sum of reciprocals — useful for rates and speeds (e.g. average MPG over two trips). For the same positive dataset: HM ≤ GM ≤ AM.

Skewness measures asymmetry. Positive skew means a long right tail (a few large values); negative skew means a long left tail. Zero skew is symmetric like a normal distribution. Kurtosis measures tailedness — how much of the variance comes from extreme values. Excess kurtosis = kurtosis − 3, so a normal distribution has excess kurtosis of 0. Positive excess = heavy tails (more outliers); negative excess = light tails.

Using the Tukey 1.5 × IQR rule. The lower fence is Q1 − 1.5·IQR and the upper fence is Q3 + 1.5·IQR. Any value outside [lower fence, upper fence] is flagged as an outlier. This is the same rule that box-plot whiskers use. Outliers aren't always errors — they can be the most interesting data points.

CV = (standard deviation ÷ mean) × 100%. It's a unit-free way to compare variability across datasets with different scales. A CV of 10% on heights vs 10% on incomes means both have the same RELATIVE spread, even though the absolute SDs are very different. Don't use it if the mean is zero or negative.