📊 Statistics

Descriptive statistics, regression models, and hypothesis tests. All commands accept lists in {1,2,3} syntax.

✓ 35 Implemented ⏳ 26 Coming Soon

Descriptive Statistics — Implemented

Mittelwert( <Liste> )

Aliases: mean, Mean

✓ Done

Returns the arithmetic mean of all values in the list.

Example

Mittelwert({1, 2, 3, 4, 5})       → 3
Mittelwert({10, 20, 30})           → 20

Median( <Liste> )

Aliases: median

✓ Done

Returns the median. For even-length lists, returns the average of two middle values.

Example

Median({1, 3, 5, 7, 9})           → 5
Median({1, 2, 3, 4})               → 2.5

Modalwert( <Liste> )

Aliases: mode, Mode

✓ Done

Returns the most frequently occurring value in the list.

Example

Modalwert({1, 2, 2, 3, 3, 3})     → 3

Standardabweichung( <Liste> )

Aliases: sd, stdev

✓ Done

Population standard deviation (divides by n).

Example

Standardabweichung({2, 4, 4, 4, 5, 5, 7, 9})  → 2

StichprobenStandardabweichung( <Liste> )

Aliases: samplesd

✓ Done

Sample standard deviation (divides by n−1). Use this when working with a sample, not the full population.

Example

StichprobenStandardabweichung({1,2,3,4,5})   → 1.5811

Varianz( <Liste> )

Aliases: variance

✓ Done

Population variance (σ²). Square of population standard deviation.

Example

Varianz({2, 4, 4, 4, 5, 5, 7, 9})   → 4

Stichprobenvarianz( <Liste> )

Aliases: samplevariance

✓ Done

Sample variance (s²), divides by n−1.

Example

Stichprobenvarianz({1, 2, 3, 4, 5})   → 2.5

GeometrischerMittelwert( <Liste> )

Aliases: gmean, GeometricMean

✓ Done

Returns the geometric mean: n-th root of the product of all values.

Example

GeometrischerMittelwert({1, 2, 4, 8})   → 2.828

HarmonischerMittelwert( <Liste> )

Aliases: hmean, HarmonicMean

✓ Done

Returns the harmonic mean: n / Σ(1/xᵢ). Useful for averaging rates.

Example

HarmonischerMittelwert({1, 2, 4})   → 1.714

Effektivwert( <Liste> )

Aliases: rms, RMS

✓ Done

Root Mean Square: √(Σxᵢ²/n). Commonly used in physics and engineering.

Example

Effektivwert({3, 4, 5, 3, 2, 3, 4})   → 3.559

Q1( <Liste> ) / Q3( <Liste> )

Aliases: q1, Quartile1 / q3, Quartile3

✓ Done

First and third quartile using the Moore & McCabe method.

Example

Q1({1, 2, 3, 4, 5, 6, 7})   → 2
Q3({1, 2, 3, 4, 5, 6, 7})   → 6

Perzentil( <Liste>, <p> )

Aliases: percentile, Percentile

✓ Done

Returns the p-th percentile (0 ≤ p ≤ 100).

Example

Perzentil({1, 2, 3, 4}, 25)   → 1.25
Perzentil({1, 2, 3, 4}, 75)   → 3.25

Summe( <Liste> ) / Produkt( <Liste> )

Aliases: sum, Sum / product, Product

✓ Done

Sum or product of all elements in the list.

Example

Summe({1, 2, 3, 4, 5})     → 15
Produkt({1, 2, 3, 4, 5})   → 120

Correlation & Covariance — Implemented

KorrelationsKoeffizient( <ListeX>, <ListeY> )

Aliases: r, PearsonR

✓ Done

Pearson correlation coefficient (−1 to 1). Measures linear association between two variables.

Example

KorrelationsKoeffizient({1,2,3},{2,4,5})   → 0.9819

Kovarianz( <ListeX>, <ListeY> )

Aliases: covariance

✓ Done

Population covariance of two data series.

Example

Kovarianz({1,2,3}, {1,3,7})   → 2

RQuadrat( <ListeX>, <ListeY> )

Aliases: r2, RSquared

✓ Done

Coefficient of determination R². r² = 1 means perfect linear fit.

Example

RQuadrat({1,2,3}, {2,4,5})   → 0.9641

Spearman( <ListeX>, <ListeY> )

Aliases: spearman, SpearmanR

✓ Done

Spearman rank correlation — measures monotonic relationship, robust to outliers.

Example

Spearman({1,2,3,4,5}, {5,6,7,8,7})   → 0.82

Sxx( <Liste> ) / Sxy( <ListeX>, <ListeY> ) / Syy( <Liste> )

Aliases: SigmaXX, SigmaXY, SigmaYY

✓ Done

Sum of squared deviations: Sxx = Σ(xi−x̄)², Sxy = Σ(xi−x̄)(yi−ȳ).

Example

Sxx({1, 2, 3, 4, 5})   → 10

Regression — Implemented

Trend( <ListeX>, <ListeY> )

Aliases: Trendlinie, LinearRegression

✓ Done

Linear regression (least squares). Returns equation y = mx + b.

Example

Trend({1,2,3,4,5}, {2,4,5,4,5})
→ y = 0.7000x + 1.5000

TrendPoly( <ListeX>, <ListeY>, <Grad> )

Aliases: PolynomialRegression

✓ Done

Polynomial regression of specified degree.

Example

TrendPoly({1,2,3,4}, {1,4,9,16}, 2)   → Degree-2 polynomial

TrendExp( <ListeX>, <ListeY> )

Aliases: TrendExp2, ExponentialRegression

✓ Done

Exponential regression: y = a·e^(bx).

Example

TrendExp({1,2,3,4}, {2.7,7.4,20,55})
→ y = 1.0003·e^(1.0001x)

TrendLog( <ListeX>, <ListeY> )

Aliases: LogarithmicRegression

✓ Done

Logarithmic regression: y = a + b·ln(x).

Example

TrendLog({1,2,3,4}, {1,1.7,2.1,2.4})
→ y = 0.010 + 1.197·ln(x)

TrendPot( <ListeX>, <ListeY> )

Aliases: PowerRegression

✓ Done

Power law regression: y = a·x^b.

Example

TrendPot({1,2,3,4}, {1,4,9,16})
→ y = 1.000·x^2.000

TrendSin( <ListeX>, <ListeY> )

Aliases: SinusoidalRegression

✓ Done

Sinusoidal regression. Estimates amplitude and vertical offset.

Example

TrendSin({0,1,2,3,4}, {1,3,1,-1,1})
→ A=2.0000, k=1.0000

Hypothesis Tests — Implemented (basic)

GaussTest( <mu0>, <sigma>, <Liste> )

Aliases: ztest, ZTest

✓ Done

One-sample z-test. Tests whether the sample mean differs from mu0 with known sigma. Returns z-statistic and p-value.

Example

GaussTest(5, 2, {4, 5, 6, 5, 4})
→ z = -0.3536, p = 0.7236

TTest( <mu0>, <Liste> )

Aliases: ttest, OneSampleTTest

✓ Done

One-sample t-test. Tests whether sample mean differs from a hypothesized value mu0 (unknown sigma).

Example

TTest(5, {4, 5, 6, 5, 4})
→ t(4) = -0.4082, p = 0.7024

TTest2( <Liste1>, <Liste2> )

Aliases: WelchTTest, TwoSampleTTest

✓ Done

Welch's two-sample t-test. Compares means of two independent groups without assuming equal variances.

Example

TTest2({4,5,6,5}, {7,8,9,8})
→ t(6.0) = -5.6569, p = 0.0013

ChiQuadratTest( <Beobachtet>, <Erwartet> )

Aliases: chitest, ChiSquaredTest

✓ Done

Chi-squared goodness-of-fit test. Compares observed to expected frequencies. Returns chi² statistic and p-value.

Example

ChiQuadratTest({25,30,20,25}, {25,25,25,25})
→ χ²(3) = 2.0000, p = 0.5724

Coming Soon — Hypothesis Tests & CIs

TTestGepaart( <Liste1>, <Liste2>, <Seite> )

⏳ Soon

Paired t-test. For related samples (before/after). Seite: "<", ">" or "!=".

Planned Syntax

TTestGepaart({10,12,14}, {11,13,16}, "!=")  → {p-value, t-stat}

ANOVA( <Liste>, <Liste>, ... )

⏳ Soon

One-way ANOVA for comparing means across multiple independent groups. Returns {p-value, F-statistic}.

Planned Syntax

ANOVA({1,2,3}, {4,5,6}, {7,8,9})  → {p-value, F}

GaussSchaetzer( <Liste>, <sigma>, <Niveau> )

⏳ Soon

Z-confidence interval for the mean with known sigma. Niveau = confidence level (e.g. 0.95).

Planned Syntax

GaussSchaetzer({1,2,3,4,5}, 1, 0.95)  → {lower, upper}

TMittelwertSchaetzer( <Liste>, <Niveau> )

⏳ Soon

t-confidence interval for the mean with unknown sigma.

Planned Syntax

TMittelwertSchaetzer({1,2,3,4,5}, 0.95)  → {lower, upper}

GaussAnteilTest / GaussAnteilSchaetzer

⏳ Soon

Proportion z-test and confidence interval. For testing whether a sample proportion differs from a hypothesized value.

Planned Syntax

GaussAnteilTest(0.45, 200, 0.5, "!=")  → {p-value, z}
GaussAnteilSchaetzer(0.45, 200, 0.95)  → {lower, upper}

SQA( <Punktliste>, <Funktion> )

⏳ Soon

Sum of squared deviations (SSE) from a given function. Used to evaluate goodness-of-fit.

GebundenerRang( <Liste> ) / OrdinalRang( <Liste> )

⏳ Soon

GebundenerRang: Tied ranks — equal values get average rank.
OrdinalRang: Unique ranks — equal values get consecutive ranks.

Planned Syntax

GebundenerRang({3, 2, 2, 1})  → {4, 2.5, 2.5, 1}
OrdinalRang({3, 2, 2, 1})     → {4, 2, 3, 1}

TrendLogistisch( <ListeX>, <ListeY> )

⏳ Soon

Logistic regression: y = a / (1 + b·e^(−kx)). Useful for S-curve data like growth/adoption models.