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Statistics

Compute (weighted or unweighted) statistical averages for data with optional uncertainties.

Desktop-only statistics workflows such as covariance/correlation matrices, grouped statistics, Bootstrap confidence intervals, hypothesis tests, and time-series smoothing are documented in the Desktop statistics guide.

Quick Workflow

  1. Input data: provide a single-column table (uncertainty is optional)

    A
1152842742.723(12)
1152842742.740(18)
1152842742.727(14)

  2. Choose statistics mode:

    • Simple mean: arithmetic mean
    • Descriptive statistics: mean, optional trimmed mean, spread, quantiles, MAD, skewness, and excess kurtosis
    • Sample variance: enable “use sample standard deviation”
    • Weighted variance: enable “use weighted variance”

  3. Review results:

    • mean ± standard error
    • 95% mean confidence interval
    • min / max / standard deviation
    • median, Q1/Q3, IQR, MAD, skewness, excess kurtosis, and optional trimmed mean in descriptive mode
    • effective sample size (when applicable, Kish formula)

Mode Notes

Simple mean

Computes the arithmetic mean and standard deviation.

Sample variance

Uses the sample standard deviation (denominator n-1).

Confidence interval

Unweighted modes report a 95% Student-t confidence interval for the mean using sample_std/sqrt(n), even when population mode is selected for displayed variance. Weighted mode reports a known-sigma normal interval using sqrt(1/Σwᵢ) unless a σ=0 anchor is active.

Descriptive statistics

Computes count, mean, optional trimmed mean, standard error, standard deviation, variance, min/max, median, Q1/Q3, IQR, MAD, skewness, and excess kurtosis. Quantiles use Hyndman-Fan type 7 interpolation. Sample variance requires n>=2, sample skewness requires n>=3, sample excess kurtosis requires n>=4, and zero-variance data reports skewness/kurtosis as unavailable diagnostics. Trimmed mean sorts finite values, removes floor(n * trim_fraction) values from each tail, and averages the remaining values. Blank or 0 disables trimming; invalid or too-large fractions are rejected.

Weighted variance

Computes weighted statistics using the provided uncertainties:

  • Weight: w = 1/σ² (rows with missing σ are skipped)
  • Weighted mean: x̄_w = Σ(wᵢ xᵢ) / Σwᵢ
  • Standard error of the weighted mean: SE(x̄_w) = sqrt(1 / Σwᵢ)
  • Weighted standard deviation (scatter): numerator uses Σ wᵢ (xᵢ-x̄_w)²; in sample mode the denominator is Σwᵢ - Σwᵢ²/Σwᵢ (in population mode it is Σwᵢ)

Edge cases:

  • If σ=0 exists: it is treated as an “infinite-weight anchor” (mean/uncertainty come from that point); conflicting σ=0 values are rejected