Interquartile Range Calculator
Measures the width of the middle half of an ordered dataset using linearly interpolated quartiles. The form displays IQR = Q3 - Q1 beside interquartile range, using a worked condition that can be recalculated with the labeled inputs.
Define the data behind interquartile range
Interquartile range
Purpose of this interquartile range calculation
The interquartile range page measures the width of the middle half of an ordered dataset using linearly interpolated quartiles.
Interquartile range is limited to the statistical quantity named by the result panel. The interquartile range calculation does not silently add a population, time horizon, causal direction, or decision threshold that is absent from the fields.
How the inputs shape interquartile range
- Dataset: For interquartile range, the displayed dataset sequence is 12, 15, 18, 18, 21, 24, 27, 30. Preserve dataset order when interquartile range depends on pairing, lag, rank, or time position, and distinguish an observed zero from a missing dataset entry.
The entries used for interquartile range must refer to one coherent analysis condition. Combining incompatible populations, periods, or measurement definitions can produce valid interquartile range arithmetic for a nonexistent study.
From inputs to interquartile range
For interquartile range, match every symbol in the relationship to a labeled field before substituting numbers. Interquartile range is reported in the scale implied by the inputs and formula.
While checking interquartile range, use dataset observations from one defined analysis set rather than totals copied from incompatible groups.
Worked values for interquartile range
The default interquartile range condition is Dataset = 12, 15, 18, 18, 21, 24, 27, 30.
For the sample values, Q1 is 17.25 and Q3 is 24.75, so the IQR is 7.5.
The live calculator reports Interquartile range 7.5 · Q1 17.25 · Q3 24.75. Repeating one intermediate step from IQR = Q3 - Q1 provides a fixed interquartile range reference check for later code changes.
The surrounding workflow may also require range to mean ratio, dataset quartiles, and winsorized mean.
Assumptions behind interquartile range
Quartile software can use different conventions. This page uses the common type-7 linear interpolation rule.
For interquartile range, the result summarizes the observations supplied to this page; extending it to a wider population requires a sampling argument that the arithmetic cannot provide.
A second check on interquartile range
When interpreting interquartile range, check the observation definition, missing-value treatment, and measurement scale before treating a descriptive statistic as comparable across datasets.
As a second check for interquartile range, outliers, ties, ordering, and missing entries can affect interquartile range even when the number of observations stays unchanged.
A practical stress test for interquartile range
Change dataset while holding the remaining entries fixed, then state why the direction and size of the interquartile range change are plausible from IQR = Q3 - Q1.
Repeat the interquartile range exercise with dataset. If a modest defensible change materially alters the interpretation, report both conditions rather than presenting that interquartile range scenario as exact.
Where a plausible interquartile range can go wrong
Before accepting interquartile range, compare every entered value with its label, unit, and allowed domain after reading the printed relationship from left to right.
For interquartile range, do not substitute zero for an unobserved value; missingness and a measured zero describe different data.
Another interquartile range failure occurs when a rounded output is reused as though it were the original measurement. Carry guard digits through calculations that depend on interquartile range, then round only the reported value.
What to record with interquartile range
Report interquartile range using IQR = Q3 - Q1, followed by the entered values, units, exclusions, and analysis date. Name the interquartile range population or dataset boundary instead of leaving it implicit.
Keep the full calculator output with the record, including Interquartile range 7.5 · Q1 17.25 · Q3 24.75. A later interquartile range review can then distinguish a changed input from a different convention or software implementation.
Questions about interquartile range
Which input deserves the closest boundary check?
For interquartile range, start with dataset. Confirm the interquartile range units and allowed domain because a valid-looking entry can still describe the wrong statistical setup.
Why could another program report a different interquartile range?
A different convention for rounding, tails, ties, interpolation, parameterization, or missing values can change interquartile range. Compare the printed interquartile range formula and its input definitions before treating either output as wrong.
What does interquartile range represent on this page?
It is the quantity produced by IQR = Q3 - Q1 from the displayed dataset. This page measures the width of the middle half of an ordered dataset using linearly interpolated quartiles.
What should be saved with interquartile range?
Save the entered values and units for dataset, along with the analysis date, exclusions, software or formula version, and the relationship IQR = Q3 - Q1. That record is sufficient to rebuild this specific interquartile range calculation.