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Descriptive statistics tool catalogue

Jube.Service/Agent/AdvancedAnalyticsTools/DescriptiveStatistics/ is one of the ten semantic tool groups an AskJooby agent calls directly by name, covering the most basic layer of the statistics toolset: central tendency, spread, shape, quantiles, frequency tables, running and rolling series statistics, table-wide summaries and simple transforms. 83 of its 97 tools have no entry anywhere else under docs/, which means Jadek, the reply-validating agent that fact-checks every answer against the RAG-indexed corpus, can never confirm a claim that cites one of them, even when the answer is correct. This page covers all 97 tools tool by tool, grouped by the source file each tool lives in. Every tool is bound to the group name DescriptiveStatistics and gated behind the Analytics permission; none of them persist anything.

Fourteen tools in this group turn out to already be documented in depth elsewhere, each with a dedicated paragraph explaining what it computes rather than a bare name-check, because they are used as the “AdvancedAnalytics equivalent” of a step in the R walkthrough at Summary Statistics and Basic Plots in R, in the charting walkthrough at Charting, or in the Monte Carlo simulation walkthrough at Monte Carlo Simulation. This page does not duplicate those write-ups; it cites them and covers the other 83 tools in full below, organised by the same four source files the R guide’s citations already use (CentralTendencyTools, QuantileRankAndFrequencyTools, SpreadAndShapeTools, TableAndTransformTools).

Already documented elsewhere

  • Mean, Median and MinimumMaximumRange (CentralTendencyTools) — Summary Statistics, Procedures 2 and 4.
  • FiveNumberSummary (QuantileRankAndFrequencyTools) — Summary Statistics, Procedure 3.
  • FrequencyTableOfCategories (QuantileRankAndFrequencyTools) — Charting, the table() equivalent.
  • Variance, StandardDeviation, InterquartileRange, Skewness, ExcessKurtosis and Kurtosis (SpreadAndShapeTools) — Summary Statistics, Procedures 3, 7 and 10.
  • DescribeColumn, SummariseColumns and ZScores (TableAndTransformTools) — Summary Statistics, Procedures 7 and 8, and Monte Carlo Simulation.

A convention shared by almost every tool below: a bool ignoreMissing parameter (default false unless stated otherwise) controls whether a NaN in values is dropped and counted in the result’s MissingIgnored/MissingCount field, or rejected outright as malformed input. Series-shaped tools (the cumulative, rolling and transform tools) instead let a NaN pass through unchanged at the same position in the output rather than dropping it, so the series stays the same length as the input; this is called out per tool below as “missing entries stay NaN.”

Central tendency, extremes and location (CentralTendencyTools)

WeightedMean computes the arithmetic mean with each value counted in proportion to a supplied non-negative weights array of the same length — a value weighted 0 contributes nothing, and the weights need not sum to 1; they must sum to something above 0.

TrimmedMean discards the lowest and highest trimFraction share of the sorted values from each tail (0 up to but excluding 0.5, default 0.1) before averaging what remains, a middle ground between the ordinary mean’s full use of the data and the median’s full resistance to outliers.

WinsorisedMean is the same idea but replaces, rather than deletes, the extreme winsorFraction share in each tail with the nearest retained value (default 0.05 per tail), which limits outlier influence while keeping the original sample size.

GeometricMean computes the n-th root of the product via logarithms, for growth factors, ratios and other multiplicative quantities; every value must be strictly positive, since a zero or negative value would make the result zero or undefined.

HarmonicMean computes the count divided by the sum of reciprocals — the correct average for rates and ratios over a fixed quantity, such as speeds over equal distances or price-to-earnings ratios — and is never larger than the geometric mean. Values must be strictly positive.

QuadraticMean (root mean square) is the square root of the mean of the squares, the typical magnitude of values that can be positive or negative, such as residuals or signal amplitude; negative values are allowed and the result is always at least the absolute value of the arithmetic mean.

PowerMean generalises all of the above to the p-th root of the mean of values raised to power order: order 1 is the arithmetic mean, 2 the quadratic mean, -1 the harmonic mean, and 0 (handled as a special case) the geometric mean; larger orders weight large values more heavily. Values must be strictly positive unless order is a positive even integer, in which case negative values are safe because they are squared away.

ContraharmonicMean (the Lehmer mean) is the sum of x^order over the sum of x^(order-1) (default order 2, the classic contraharmonic mean, up to 20); because it weights large values by themselves it is always at least the arithmetic mean, and it answers “what is the mean group size seen by a randomly chosen member” — the sum of the values must not be zero.

ExponentialWeightedMean computes a recency-weighted mean of a time-ordered series in which the most recent observation (the last element) carries the greatest weight and older observations decay geometrically, controlled by a smoothing factor alpha strictly between 0 (exclusive) and 1 (inclusive, default 0.3): near 1 it tracks the latest values closely, near 0 it approaches the plain mean.

GrandMean combines several already-computed group means into one overall mean, weighting each by its own sampleSizes — use it when only per-group summaries, not the raw data, are available; every sample size must be at least 1 and no group mean may be NaN.

Trimean is Tukey’s robust location estimate, (Q1 + 2*median + Q3) / 4, blending the median with the quartiles (computed by linear interpolation) so it copes better with skewed data than the median alone.

Midhinge is the average of the lower and upper quartiles; comparing it with the median shows asymmetry in the middle of the distribution specifically, since a large gap between them signals the two quartiles are not symmetric around the median.

Minimum and Maximum return the smallest and largest value respectively, each with Count and MissingIgnored.

ArgumentOfMinimum and ArgumentOfMaximum locate where the extreme value sits rather than just its value: each returns the zero-based Index of the first occurrence (ties broken by position) in the original array together with the Value there, so the record behind an extreme low or high can be traced back even when ignoreMissing has dropped other rows — the index returned always refers to the original, unfiltered array.

Sum totals a list of numbers for aggregate amounts; an overflow beyond roughly 1.8e308 returns infinity rather than throwing.

Product multiplies a list of numbers, for example compounding growth factors; very long lists can overflow to infinity or underflow to 0, in which case GeometricMean or working on logarithms directly is the safer choice.

CountValues profiles data quality before any statistic that would fail on gaps: total, valid (non-missing), missing, infinite, distinct, zero, positive and negative counts, plus MissingFraction (missing over total). It takes no ignoreMissing flag because it is designed to run on data containing NaN.

ModeOfNumbers returns every value tied for the highest frequency in Modes (ascending), the shared Frequency, and IsUnique (false when more than one mode exists). For genuinely continuous data where every value differs, every value is its own mode with frequency 1, so the description recommends binning first in that case.

ModeOfCategories is the same idea for text labels, compared exactly and case-sensitively; an empty string is a valid label in its own right, while null is treated as missing when ignoreMissing is set.

WeightedMode finds the value with the largest total weight rather than the largest count, with ties again returned together in Modes; Frequency here is the summed weight rounded to the nearest whole number, so Count (not Frequency) is the field to read for the actual number of observations. Weights must be finite and non-negative.

CircularMean computes the mean direction of cyclical data — hour of day, day of week, month, compass bearing — where, for example, 23:00 and 01:00 are close together even though an ordinary mean of the hours 23 and 1 gives 12. The cycle length is set by unit (Radians, Degrees, Hours24 default, Days7 or Months12); the result is NaN when the directions cancel out exactly (resultant length near 0), which CircularSummaryStatistics below makes visible.

CircularSummaryStatistics gives a fuller cyclical profile: mean direction, median, mean resultant length (0 to 1, near 1 meaning values cluster at one time of the cycle, near 0 meaning they spread evenly around it), circular variance (1 - resultant length), circular standard deviation, angular deviation, concentration, skewness and kurtosis. Use it to test whether activity concentrates at particular times rather than spreading evenly through the cycle; directions come back in the chosen unit while the spread measures are in radians.

Quantiles, ranks and frequency tables (QuantileRankAndFrequencyTools)

Quantile returns the value below which a given cumulative probability (0 to 1) of the data falls — for example 0.9 for the 90th percentile — interpolated between neighbouring sorted values by the chosen interpolation rule (Linear, the spreadsheet default, or Weibull, used by some statistics packages).

Quantiles returns several such quantiles from one call, one per entry of a probabilities array, in the same order; Percentiles is the same thing expressed as percent levels from 0 to 100 (more convenient for reporting) rather than 0-to-1 probabilities.

EqualProbabilityCutPoints returns the parts - 1 interior cut points that divide the data into parts (2 to 1000) equal-sized groups — 4 for quartiles, 10 for deciles, 100 for percentiles — together with the matching probabilities, for binning a variable into equal-frequency bands.

InterpercentileRange is the distance between two arbitrary percentiles, such as the 10th-to-90th range, which ignores the most extreme tails while remaining a flexible, outlier-resistant spread measure; lowerPercent must be below upperPercent, both between 0 and 100.

PercentileRankOfValue finds where a single score sits within a reference values array, as a percentile rank from 0 to 100 (the percent of observations below it) — for example, stating that a transaction is larger than 97 percent of a customer’s history. kind controls how ties at the exact score are handled: Weak counts values at or below the score, Strict only values strictly below, Mean (the default) averages the two, which is the usual choice when ties matter. The score need not itself appear in the reference data.

PercentileRanksOfValues applies that same ranking to every value against the rest of its own array in one call, in the original order, converting a skewed variable onto a uniform 0-to-100 scale, or scoring each observation relative to its peers; a NaN entry stays NaN in the output and is excluded from the reference set used to rank everyone else.

RanksOfValues returns the rank of each value (1 is smallest, unless descending is set) with a choice of tie handling (ties): Average (the standard for rank-based statistics, giving tied values the mean of their ranks), Minimum, Maximum, Dense (no gaps between successive ranks) or Ordinal (a distinct rank per position even among ties). HasTies and TiedGroups report whether and how much tying occurred; NaN entries stay NaN and are excluded from ranking.

ThresholdShare counts and proportions observations above, below and equal to a threshold — for example the share of transactions over a reporting limit — with proportions computed relative to the non-missing count, useful for exceedance rates and simple rule-hit-rate estimates.

CumulativeSum, CumulativeProduct, CumulativeMaximum and CumulativeMinimum each return a running statistic over a series in original order: element i is, respectively, the sum, product, maximum or minimum of elements 0 through i (a high- or low-water mark for the latter two). CumulativeProduct is for compounding growth factors into a cumulative index and can overflow to infinity or underflow to 0 on a long series. In all four, a NaN entry stays NaN at its own position and is skipped when computing the values around it.

RollingStatistic computes a chosen statistic (Mean, Sum, Median, Minimum, Maximum, StandardDeviation, Variance, Range, Skewness or Count) over a trailing window of the last N observations at every position — a moving average or moving volatility of a time-ordered series. Position i uses observations i - window + 1 through i; NaN values inside a window are skipped, and the output stays NaN until at least minPeriods valid values are available (0 or less means the full window) or until the chosen statistic has enough values to be defined at all (standard deviation and variance need 2, skewness needs 3). The combination of series length and window is capped to bound the work done.

ExpandingStatistic is the same set of statistics computed over an expanding window — everything seen so far at each position, rather than a fixed trailing window — useful for watching an estimate settle as data accumulates; NaN values are skipped and the output stays NaN until minPeriods (default 1) valid values exist. It is capped at 20,000 observations; use CumulativeSum directly for a longer running total, or RollingStatistic with an explicit window for a longer series.

ExponentialMovingAverageSeries returns one exponential-moving-average value per position of a time-ordered series: each output is alpha * current + (1 - alpha) * previous output, starting from the first value, with alpha strictly between 0 (exclusive) and 1 (inclusive, default 0.3) controlling how fast it reacts. A NaN entry is carried through as NaN at its own position and does not update the running average for what follows.

FrequencyTableOfIntegers gives value counts for integer codes or discrete counts (day of week, item count, status code): each distinct value with its count, proportion, percent and cumulative share, ordered by order (ByCountDescending default, ByValueAscending or ByFirstAppearance), with maxRows limiting the rows returned and RowsOmitted reporting the rest.

FrequencyTableOfNumbers is the same table for exact numeric values rather than integer codes — the quickest way to spot repeated-amount structuring, such as many payments of exactly 9.99 or 1000.00 — matching values exactly rather than binning them, so continuous data needs a histogram instead; NaN entries are missing.

RareCategories lists the labels that occur at most maxCount times (default 1, i.e. singletons): typos, new counterparties or genuinely unusual behaviour often surface this way. Rows are ordered by count ascending then label; Total is all observations, Distinct the number of distinct labels overall (not just the rare ones), and RowsOmitted the rare labels beyond maxRows.

Spread, shape and concentration (SpreadAndShapeTools)

StandardErrorOfMean is the sample standard deviation divided by the square root of the sample size, measuring how precisely the sample mean estimates the true population mean; it shrinks as more data accumulates and needs at least 2 values. As a rule of thumb, the true mean lies within about two standard errors of the sample mean with 95 percent confidence for reasonably large samples.

CoefficientOfVariation is the standard deviation divided by the absolute mean, a unit-free relative-spread measure that lets variability be compared across variables on different scales (0.25 means the spread is 25 percent of the level); it is NaN or infinite when the mean is 0 and is only meaningful for ratio-scale data not centred on zero.

GeometricStandardDeviation is the exponential of the standard deviation of the logarithms — a multiplicative spread factor for positive, right-skewed amounts. A value of 1 means no spread; 2 means typical values lie within a factor of 2 above or below the geometric mean. All values must be strictly positive and at least 2 are required.

VarianceToMeanRatio (the index of dispersion) is the sample variance divided by the mean, applied to non-negative counts per interval: a value near 1 is consistent with a Poisson process, above 1 means over-dispersed (bursty or clustered), below 1 under-dispersed (unusually regular). It is undefined when the mean is 0.

MeanAbsoluteDeviation is the average absolute distance of values from their mean, or from their median when aroundMedian is set — a spread measure in the data’s own units that is less sensitive to outliers than the standard deviation, though still less robust than the median-based measure below.

MedianAbsoluteDeviation (MAD) is the median of the absolute distances from the median itself, a spread measure robust enough that up to half the data can be contaminated without destroying it. With scaleToNormal true (default) the raw MAD is multiplied by 1.4826 so it estimates the standard deviation under normality; false returns the raw value. A result of exactly 0 means more than half the values are identical.

QuartileCoefficientOfDispersion is (Q3 - Q1) / (Q3 + Q1), a robust unit-free relative-spread measure analogous to the coefficient of variation but built from quartiles instead of the mean and standard deviation; it is NaN when the quartiles sum to 0, and is meaningful mainly for positive, skewed data.

SumOfSquaredDeviations is the total sum of squared deviations from the mean (the “sum of squares,” SS) — the building block that variance and analysis of variance both divide down from — returned in squared units of the original data; dividing by n - 1 recovers the sample variance.

WeightedVariance and WeightedStandardDeviation compute variance and its square root when every observation carries a non-negative weights value, with weightKind choosing between Frequency weights (repeat counts, where the unbiased estimator divides by total weight minus 1) and Reliability weights (importance or probability weights, using the reliability-weights correction instead). The unbiased estimator needs a total weight above 1.

ExponentialWeightedVariance is the time-ordered, recency-weighted counterpart of ordinary variance, with the most recent observation weighted most heavily, controlled by a decay factor alpha strictly between 0 and 1 (default 0.3, larger values forgetting the past faster); a series shorter than 2 values is rejected.

PooledVariance and PooledStandardDeviation combine the variances of several groups (groups, an array of arrays, which can differ in length) into the single common-variance estimate used by equal-variance t-tests and ANOVA, averaging each group’s variance weighted by its degrees of freedom; every group needs at least 2 values. PooledVarianceFromSummaries reaches the same pooled variance from group summaries alone — sizes and variances per group — when the raw data itself is not available; every size must be at least 2 and no variance may be negative.

ShapeStatistics returns skewness, excess kurtosis and Pearson kurtosis together in one call, for judging how far a variable departs from a normal bell curve: skewness and excess kurtosis both near 0 are consistent with normality, while large positive values flag a right tail and heavy tails respectively. The unbiased forms need 4 values; the population forms need only 1.

RawMoment is the plain (non-central) moment of a given order (1 to 12) — the mean of the values raised to that power, where order 1 is the mean itself and order 2 the mean square; large values raised to high powers can overflow.

CentralMoment is the moment of a given order (1 to 12) taken about the mean rather than about 0 — order 2 is the population variance, order 3 measures asymmetry, order 4 tail weight, and order 1 is 0 by definition — using the population divisor n throughout.

StandardisedMoment divides the central moment of a given order (3 to 12 only; orders 1 and 2 are the mean and variance themselves) by the population standard deviation raised to that same order, giving a scale-free shape number: order 3 is skewness and order 4 is Pearson kurtosis, derived here from first principles rather than via the dedicated Skewness/Kurtosis tools.

EntropyOfCounts computes the Shannon entropy of a distribution supplied directly as non-negative counts or probabilities (which need not sum to 1): 0 means one category holds everything, and the maximum is the log of the category count when every category is equally likely. It returns Entropy in the chosen unit (Bits default, Nats or Hartleys), MaximumEntropy, NormalisedEntropy (entropy over maximum, 0 to 1, a measure of evenness) and Perplexity (the effective number of equally likely categories that entropy implies). Zero counts are ignored, and the total must be positive.

EntropyOfCategories computes the same Shannon entropy, but starting from a raw array of category labels whose frequencies are counted internally first — merchant categories or countries, for example — where low entropy means activity concentrates on a few categories and high entropy means it spreads evenly; null labels are treated as missing.

InequalityMeasures profiles concentration of non-negative amounts — spend, balances, transaction counts per account — in one call: the Gini coefficient (0 perfectly equal, near 1 one holder has almost everything), the Theil index, the Herfindahl-Hirschman index of shares (1/n for perfectly equal shares, 1 for total concentration), the coefficient of variation, and a Lorenz curve of cumulative population-versus-value shares at up to 101 evenly spaced points. Values must be non-negative and must not all be zero.

GiniCoefficient returns just the Gini number from the same calculation as InequalityMeasures, for when the single headline figure is all that is wanted, with the identical input constraints (non-negative, not all zero).

Table-wide summaries, correlation and transforms (TableAndTransformTools)

DescribeTable is the one-call overview of an entire numeric table before deeper analysis: a per-column summary (the same shape SummariseColumns returns), a missing-value profile, the strongest pairwise correlations (computed on rows complete in each pair, listed only when the absolute correlation is at least 0.5, up to 10 pairs), and lists of constant columns, skewed columns (absolute skewness above 1), columns with IQR-fence outliers and columns with any missing values. Use it to orient on a new dataset before choosing a deeper analysis.

TableMissingnessProfile reports exactly how much of a table is missing: per column, the present and missing counts, missing fraction and infinite-value count; and overall, how many rows are completely present, how many rows have any gap at all, the distribution of missing-cell counts per row (MissingCountPerRowDistribution[k] is the number of rows with exactly k missing cells), and the first few incomplete row indices for spot-checking. Use it before modelling to see whether gaps concentrate in a few columns or spread thinly across many rows.

ColumnCovarianceMatrix returns the sample covariance matrix of a table’s columns: entry [i][j] is how columns i and j vary together, in the product of their original units, with the diagonal holding each column’s own variance. Rows containing any missing value are rejected unless dropIncompleteRows is set, in which case they are removed and counted; at least 2 complete rows are needed. ColumnCorrelationMatrix is the unit-free counterpart, each entry a Pearson correlation between -1 and 1 with 1 on the diagonal; a constant column has an undefined correlation with everything and gives NaN throughout its row and column rather than a spurious 0 or 1.

StrongestColumnCorrelations ranks pairs of columns by the strength of their Pearson correlation rather than returning the full matrix, pairing each with its covariance, so redundant or related variables surface without scanning a whole matrix by eye. Each pair uses pairwise deletion (every row where both columns of that pair are present, independent of other columns); only pairs at or above minimumAbsoluteCorrelation (default 0.3) are kept, strongest first, up to maxPairs (default 20).

QuantilesByColumn computes the same set of quantiles for every column of a table at once, for example the 5th, 50th and 95th percentile of every variable in one call for a side-by-side distributional comparison. Missing values are excluded per column independently, with Counts reporting how many values each column actually contributed; a column with no usable values returns NaN quantiles rather than failing the whole call.

SummariseRows is the row-wise counterpart to column summaries: for every row of a table it returns the count of present values, sum, mean, minimum, maximum and standard deviation across that row’s columns, ignoring any missing cells in it — useful for row-level aggregates such as total spend across several product columns, or the spread of several model scores for one case. Standard deviation is NaN for a row with fewer than 2 present values.

SummariseByGroup splits one numeric variable by a categorical groups array and reports, per group, count, mean, median, standard deviation, minimum, maximum and sum, plus the pooled standard deviation and the grand mean across all groups combined — the natural way to compare, say, transaction amounts by channel or country. A null group label forms its own group literally named (missing) rather than being dropped; NaN values are excluded by default (ignoreMissing defaults to true here, unlike most other tools in this group) and counted.

SummariseCategories profiles a categorical variable as a whole: total, missing, distinct count, the mode(s) with their frequency, Shannon entropy in bits, normalised entropy (0 concentrated, 1 perfectly even), Gini impurity, Herfindahl index, the count of labels seen exactly once, and the top 10 labels by count. A high distinct count alongside many singletons is the signature of a near-unique identifier rather than a genuine category; null labels count as missing and are excluded from the rest of the profile.

TopShareConcentration is a Pareto-style concentration analysis of non-negative amounts in both directions at once: the share of the total held by the biggest topFractions of holders (default 1 percent, 10 percent, 20 percent), and the number of holders needed to reach given shareTargets of the total (default 50, 80, 90 percent) — for example, how many customers make up 80 percent of total value. Values must be non-negative with a positive total.

RobustZScores standardises values as (value - centre) / scale using robust estimators rather than the mean and standard deviation ZScores uses: scale selects MedianAbsoluteDeviation (default, centre the median, spread 1.4826 * MAD), InterquartileRange (centre the median, spread IQR / 1.349), or StandardDeviation (centre the mean, which defeats the purpose of robustness but is accepted for comparison). Values beyond about 3 to 3.5 on this scale are usually unusual; a series whose computed scale is exactly 0 is rejected, since nothing could be standardised against it. Missing entries stay NaN.

CentreValues subtracts the mean or median (centre, default Mean) from every value, without rescaling, to work in deviations from the typical value rather than ratios or z-scores; missing entries stay NaN.

TransformValues applies one of eleven common element-wise transforms (transform): natural log, log base 10 or 2, log(1+x), square root, cube root, square, reciprocal, absolute value, sign, negation, or a signed log(1+|x|) that preserves sign across zero. Log and square root are the usual first step to tame right-skewed amounts before further analysis. A value outside the chosen transform’s domain (log needs a strictly positive value, log1p needs greater than -1, square root needs non-negative, reciprocal needs non-zero) is rejected with the index of the first offending value named in the error; missing entries stay NaN.

ProportionsOfTotal divides every value by the sum of all of them, so the output always sums to 1 — the share of a total that each account, product or period holds. The total must not be zero; Scale in the result records what that total was.

WinsoriseValues caps extreme values at chosen percentiles rather than removing them: anything below lowerPercent (default 1) is pulled up to that percentile’s value and anything above upperPercent (default 99) is pulled down to it, keeping every observation in the series while limiting the influence of outliers on a mean or a model fit; Centre/Scale in the result hold the lower and upper cap values actually used.

FlagOutliersByZScore flags values whose z-score (value - mean) / standard deviation exceeds threshold (default 3) in either direction — simple and widely understood, but the mean and standard deviation it is built on are themselves distorted by the very outliers being sought, so FlagOutliersByMedianAbsoluteDeviation is preferred on small or heavy-tailed data. It returns IsOutlier per value in original order, the outlier indices and values, each value’s own z-score in Scores, and the LowerBound/UpperBound value limits implied by the threshold; NaN values are never flagged.

FlagOutliersByIqrFence flags values outside Tukey’s fences — below Q1 - k*IQR or above Q3 + k*IQR, with the multiplier fenceMultiplier (default 1.5 for ordinary outliers, 3 for extreme ones, the classic box-plot rule). Being built on quartiles it is robust and assumes nothing about normality, but can flag many points on strongly skewed data where the whole upper tail sits outside a fence computed from a tight box. Scores here is the signed number of IQRs a value lies beyond its nearest quartile, 0 for anything inside the box.

FlagOutliersByMedianAbsoluteDeviation flags values whose modified z-score, 0.6745 * (value - median) / MAD, exceeds threshold (default 3.5, the Iglewicz-Hoaglin recommendation). Because it is built on the median and the MAD rather than the mean and standard deviation, it stays reliable even when up to about half the data is contaminated, making it the preferred rule for messy real-world amounts. If more than half the values are exactly identical, MAD itself is 0; the tool falls back to the mean absolute deviation in that case and reports the spread actually used in Scale, rather than failing outright.