Inspect Quartiles and Outlier Fences Under One Named Convention — Free
Quartile software can disagree because its definitions differ. Sort your own observations, inspect the median-of-halves working and see which values sit outside fences you choose—without treating an outlier mark as a reason to discard data.
The proof surface
Percentage-point gap tools compare response shares. This gauge shows a distribution calculation, names its quartile convention and retains both halves and the fence rule, so a result can be reproduced rather than accepted as an opaque statistic.
Rare devicePercentage-point gap tools compare response shares. This gauge shows a distribution calculation, names its quartile convention and retains both halves and the fence rule, so a result can be reproduced rather than accepted as an opaque statistic.
Output artifactLargest dataset interquartile range with row-by-row context
Cost$0 local calculation · no card, paid key, subscription or signup · proposed filing price is not for sale
Sample, not your facts: Illustrative inputs: North trial | 4, 6, 8, 10, 12; South trial | 6, 7, 8, 9, 10. Interquartile-range fence multiplier = 1.5. Largest dataset interquartile range: 6 interquartile units. All records are invented.
Before using the quartile-fence gauge
Use a small teaching dataset whose observations share a unit and have a clear meaning. The instrument accepts signed numbers because some ordinary measurements can be below zero, but it cannot decide whether a number belongs in your study. State the convention before comparing output with a textbook or spreadsheet. This implementation excludes the median observation from both halves when the count is odd, takes the median of each half, and uses strict outside-fence comparisons. That is one reproducible convention, not a claim that every package uses it. A fence is an exploratory flag; it is not a data-cleaning instruction, a clinical threshold or a test of misconduct. Keeping the sorted observations visible in the row note helps a learner locate why a quartile moved.
Why the flat version breaks
Comparing unnamed quartile algorithms
Interpolation and median-of-halves methods can differ on small samples. State this convention before calling a software difference a wrong answer.
Dropping every fence exceedance
A fence is an exploratory calculation, not proof of an error. A rare observation may carry the very phenomenon the dataset was collected to understand.
Averaging spread across unlike units
An IQR in minutes is not directly comparable with an IQR in millimeters. The largest-row headline assumes comparable observations and units.
How to work the quartile-fence gauge
Use comparable observations
Enter at least two and at most one thousand observations per row, with a maximum of five thousand across the run. Keep a shared unit across datasets. Do not enter personal respondent data, clinical measurements or confidential research records.
Name the quartile convention
Observations are sorted numerically. The overall median is reported. For an odd count, exclude the central observation before taking medians of lower and upper halves; for an even count, split into equal halves. This convention is printed with the working.
Build and inspect the fences
IQR equals Q3 minus Q1. Lower fence equals Q1 minus multiplier times IQR, and upper fence equals Q3 plus multiplier times IQR. Values strictly outside are listed. A value exactly on a fence is not marked; the multiplier is your setting, not a universal deletion rule.
Explain a difference before changing data
Check convention, transcription and units if another program reports a different quartile. Discuss consequential analysis choices with an instructor or qualified analyst. Do not remove a flagged observation without a justified process outside this arithmetic explorer.
What the quartile-fence gauge separates
Question
Before
Inspect this instead
Comparing unnamed quartile algorithms
Interpolation and median-of-halves methods can differ on small samples. State this convention before calling a software difference a wrong answer.
Name the quartile convention
Dropping every fence exceedance
A fence is an exploratory calculation, not proof of an error. A rare observation may carry the very phenomenon the dataset was collected to understand.
Build and inspect the fences
Averaging spread across unlike units
An IQR in minutes is not directly comparable with an IQR in millimeters. The largest-row headline assumes comparable observations and units.
Explain a difference before changing data
This quartile-fence gauge replaces a manual count or calculation, not source verification or the responsible person’s review.
Run it on the samples, right here
FIRST-LOAD
HYPOTHESIS / PROTOTYPE — checkout unavailable. Calculation is local. A draft is saved automatically in this browser profile when storage is available; Reset to sample clears it. Optional Pro history stores only five summaries and has its own deletion control. State links encode your inputs and can remain in browser history, clipboard or recipients’ records; share only non-sensitive rows. Optional external AI formatting leaves this device. The required site analytics beacon reports page activity; shared URLs contain encoded inputs. Do not treat an encoded URL as private. The calculator has no input-collection endpoint.
Educational descriptive arithmetic only, not statistical inference, research validation, diagnosis or a data-deletion recommendation. The median-of-halves convention is explicit and may differ from other software. Use non-sensitive teaching data and ask an instructor or qualified analyst before making consequential analysis or exclusion decisions.
Data note: The quartile-fence gauge processes dataset label | comma-separated observations locally. Starter/sample selection and Run compute in this tab; no input is sent by the calculator. A local draft may be saved; explicit state-link sharing or optional external AI formatting can disclose inputs. Use non-sensitive labels.
Go deeper: the companion app files the same reading as a meter band gauge
The article demo above runs without limits. The companion app keeps a local history, exports the rows as CSV, prints the quartile-fence gauge reading, and holds your drafts on this device — one complete free app run; the proposed $4 one-time filing layer is not for sale.
The quartile-fence gauge answer stays complete for free. The proposed $4 one-time filing layer adds row CSV, print and five local reading summaries, not hidden answers. Checkout is unavailable; the article demo remains unlimited.
Educational descriptive arithmetic only, not statistical inference, research validation, diagnosis or a data-deletion recommendation. The median-of-halves convention is explicit and may differ from other software. Use non-sensitive teaching data and ask an instructor or qualified analyst before making consequential analysis or exclusion decisions.
What this is built on
Method: IQR equals Q3 minus Q1. Lower fence equals Q1 minus multiplier times IQR, and upper fence equals Q3 plus multiplier times IQR. Values strictly outside are listed. A value exactly on a fence is not marked; the multiplier is your setting, not a universal deletion rule.
All sample records, dates, quantities and labels are invented. No outside policy, contract, rate, clock offset, measurement or accessibility standard is represented as verified.
Google’s official pricing documentation, fetched 2026-09-30, says AI Studio is free in available regions. Optional formatting may require a Google account; manual local entry requires none. Limits can change and free-tier content may be used to improve products. Do not send private records.
Before: quartile differences looked like unexplained software disagreement. After: the median-of-halves convention and its exploratory fences can be followed by hand.
Three worked readings, with different inputs
Sample A — typical inputs
North trial | 4, 6, 8, 10, 12
South trial | 6, 7, 8, 9, 10
North trial has median eight. Under this instrument’s median-of-halves convention, the middle observation is excluded from both halves: Q1 is the median of four and six, five; Q3 is the median of ten and twelve, eleven. IQR is six. South trial has Q1 of 6.5 and Q3 of 9.5, an IQR of three. The largest IQR is six. A different software quantile convention can produce different quartiles without either calculation being a transcription error.
Sample B — changed plan
North trial | 1, 2, 3, 4, 5, 40
South trial | 6, 7, 8, 9, 10
With six observations, North trial’s lower half is one, two, three and its upper half is four, five, forty. Q1 is two, Q3 is five and IQR is three. At a 1.5 multiplier, fences are minus 2.5 and 9.5; forty is outside the upper fence. The row names it as an arithmetic fence exceedance, not an invalid measurement. A large observation can be real and important; inspect the source and the study context rather than deleting it to tidy a chart.
Four identical sevens have zero IQR and no value outside their coincident fences. For a two-value dataset, the halves are the single values six and eight, producing Q1 six, Q3 eight and IQR two. The headline therefore reports two. These small datasets are explicit arithmetic cases, not evidence of a stable population distribution. At least two observations are required; a lone value cannot support this chosen two-half comparison.
Optional AI formatting, never the calculation
Manual entry completes this quartile-fence gauge for free without signup. If available to you, the free AI Studio interface linked in the sources may format fictional or non-sensitive notes; external access may require an account. No API key or AI call is built into this tool. Free-tier content may be used to improve products. Review each cell and transcribe it to the labeled row schema; do not paste the JSON object into the row box.
Format only these fictional or non-sensitive notes for a quartile-fence gauge. Return strict JSON shaped as {"rows": [{"label": "string", "cells": ["string"]}], "setting": "string"}. The columns are dataset label | comma-separated observations; the setting is Interquartile-range fence multiplier. Keep all supplied strings and quantities exactly; do not calculate, infer missing entries, invent dates or add advice. If any required value is missing, return an empty rows array and ask me for it separately. I will verify every cell against my source and manually transcribe rows using vertical bars before running the local calculator.
An AI response is not executed, fetched or trusted as a result. Missing values remain questions; the strict local parser checks the rows you actually enter.