Method and source check
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Editorial check of method and sources; this is not professional review or advice.
Method
The calculator validates at least two finite numbers, sorts them, and reports the minimum, 25th percentile, median, 75th percentile, and maximum. Percentiles use linear interpolation with zero-based position h = (n − 1)p; range and IQR are derived from those values.
Q(p) = x⌊h⌋ + (h − ⌊h⌋)(x⌊h⌋+1 − x⌊h⌋), h = (n − 1)p
IQR = Q3 − Q1
range = maximum − minimum
Variables and units
- x
- the data sorted in ascending order
- p
- 0.25, 0.50, or 0.75
- n
- number of data values
Worked example
For 1, 2, 3, 4: minimum = 1, Q1 = 1.75, median = 2.5, Q3 = 3.25, maximum = 4, IQR = 1.5, and range = 3.
Limitations
Minimum, Q1, median, Q3, maximum, range, and IQR are rounded to at most four decimal places. The result card displays these numbers without trailing zero padding; the sorted input values are retained unrounded.
- Quartile conventions differ among books and software. This calculator uses the stated linear-interpolation convention, so Q1 and Q3 can differ from tools that use lower- and upper-half medians.
- Input 1, 2, 3, 4 returns minimum 1, Q1 1.75, median 2.5, Q3 3.25, maximum 4, IQR 1.5, and range 3 under h = (n − 1)p interpolation.
- Input 1, 3 returns minimum 1, Q1 1.5, median 2, Q3 2.5, maximum 3, IQR 1, and range 2.
- A single number or a nonfinite token fails validation; at least two finite numbers are required.