Five-Number Summary and Box Plot

Install and import#

npm install fintech-algorithms

import { fiveNumberSummaryAndBoxPlot } from "fintech-algorithms/foundations/location-ranking-and-exploratory-summaries/five-number-summary-and-box-plot";

Signature#

fiveNumberSummaryAndBoxPlot(input)

Produces the minimum, three quartiles, and maximum of a numeric series, the Tukey 1.5-IQR fences drawn from them, and the observations lying outside those fences.

Parameters#

Returns#

{ fiveNumberSummary: number[]; fences: [number, number]; outliers: number[] }

fiveNumberSummary is [minimum, q1, median, q3, maximum], fences is [q1 - 1.5 * iqr, q3 + 1.5 * iqr], and outliers lists the observations strictly outside the fences in the caller's original order.

Errors#

• When input is null, an array, or not an object — throws TypeError
• When values is missing, is not an array, or is empty — throws RangeError
• When any entry of values does not coerce to a finite number — throws RangeError

Complexity: time O(n log n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

{
  "values": [1, 2, 2, 4, 9],
  "weights": [1, 1, 2, 1, 1],
  "trimProportion": 0.2,
  "bins": 4
}

Call#

fiveNumberSummaryAndBoxPlot(input)

Returns#

object with 2 fields: fiveNumberSummary, fences

{
  "fiveNumberSummary": [1, 2, 2, 4, 9],
  "fences": [-1, 7]
}

Diagrams#

Calculation flow#

flowchart LR
    A["Finite observations"] --> B["Name units and scope"]
    B --> C["Freeze: IQR = Q3−Q1; inner fences = Q1−1.5IQR and Q3+1.5IQR; whiskers stop at extreme observations within fences"]
    C --> D["Calculate full precision"]
    D --> E{"Boundary satisfied?"}
    E -->|Yes| F["Report five numbers [1, 2, 2, 4, 9] · fences [−1, 7] · possible outlier [9]"]
    E -->|No| G["Abstain and repair contract"]
    F --> H["Pair with distribution context"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• Box Plot
• Percentile Definitions
• Historical-example decision

The rest of the Location, Ranking, and Exploratory Summaries family#

• Count, Sum, Minimum, Maximum, and RangeReduces one numeric series to the five headline aggregates: how many observations there are, their total, the smallest and larg…
• Arithmetic MeanDivides the sum of a numeric series by the number of observations and reports both the mean and the count it was divided by.
• Weighted MeanComputes a weighted average of values using the parallel weights series, dividing the sum of value-times-weight products by…
• Median and ModeReports the middle of a numeric series and its most frequent values, tallying exact equality so a tie produces several modes ra…
• Trimmed and Winsorized MeansCuts the same number of observations off each tail of the sorted series and averages what is left, then averages again with tho…
• Percentiles, Quantiles, and QuartilesReturns the three quartiles of a numeric series and the interquartile range between the first and third, using linear interpola…
• Ranks, Ties, and Percentile RankAssigns each observation its position in the sorted series, giving tied observations the average of the positions they span, an…
• Frequency Tables and Relative FrequencyCounts how often each distinct value occurs in a numeric series and expresses those counts as shares of the total.
• Histograms and Empirical Distribution FunctionsSplits the observed span into equal-width bins and counts the observations in each, alongside the empirical distribution functi…