Statistics calculator: mean, median, standard deviation, quartiles and percentiles

Statistics calculator for a numeric array in one call: count, sum, mean, median, mode, variance and standard deviation honouring ddof (default 1, the sample form; 0 gives the population form) plus always-population *_population fields, min, max, range, the quartiles and interquartile range, skewness, kurtosis, and any requested percentiles. Percentiles use a named interpolation method so the result is reproducible rather than implementation-defined.

Output (data): n, sum (number|null), mean (number|null), median (number|null), mode ([] or null, null when every value is distinct), ddof (integer), variance (number|null: n-ddof divisor, null when n <= ddof), stdev (number|null, null when n <= ddof), variance_population (number|null), stdev_population (number|null), min, max, range (number|null), q1 (number|null), q3 (number|null), iqr (number|null), skewness (number|null, null when n < 3 or the variance is 0), kurtosis_excess (number|null, null when n < 4 or the variance is 0), percentiles {<p>: number|null}, method, outliers_tukey []. Any computed number is null when the result is not finite, i.e. overflows the double range (e.g. values=1e308,1e308)

Deterministic: identical input returns identical output, so the response is served with Cache-Control: private, max-age=31536000, immutable (the paying client may cache it indefinitely; shared caches must not, because the response is paid).

Price: $0.05 USDC per call (x402, Base). Route contract version 1.0.0. Docs: https://api.duoleads.com/docs#num-stats