Mathematics · Statistics
Interquartile Range Calculator
Calculate the middle-50-percent spread for six values.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Q₁=2; Q₃=5.
- IQR=5−2=3.
Understand Interquartile range
One idea, three depths
Choose how deeply to explain Interquartile range
Interquartile range: Calculate the middle-50-percent spread for six values.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Interquartile range to answer this question: calculate the middle-50-percent spread for six values? Enter Value 1, Value 2, Value 3, and 3 other inputs; the calculator shows Interquartile range. For example: 1–6 has IQR=5−2=3. The answer tells you Interquartile range.
Age 15Explain it to a 15-year-oldConnect it to the formula
The IQR measures central spread while reducing sensitivity to extremes. The rule is IQR=Q₃−Q₁. Its input values are Value 1, Value 2, Value 3, Value 4, Value 5, Value 6, and the main result is Interquartile range. For example: 1–6 has IQR=5−2=3.
CollegeExplain it at college levelState the model precisely
This calculator evaluates the stated interquartile range relation over the valid real-number domain stated below. The implemented relation is IQR=Q₃−Q₁, evaluated from Value 1, Value 2, Value 3, Value 4, Value 5, Value 6 to produce Interquartile range. The IQR measures central spread while reducing sensitivity to extremes. Quartile conventions can differ for other sample sizes.
Inputs and valid domain
- Value 1 must be a finite real number.
- Value 2 must be a finite real number.
- Value 3 must be a finite real number.
- Value 4 must be a finite real number.
- Value 5 must be a finite real number.
- Value 6 must be a finite real number.
Important boundary: Quartile conventions can differ for other sample sizes.
The formula
IQR=Q₃−Q₁
How the calculator works through it
It substitutes Value 1, Value 2, Value 3, Value 4, Value 5, Value 6 into the formula and exposes every numerical step above. The main output is Interquartile range, accompanied by Q₁, Q₃.
Read the result correctly
The Interquartile range is the direct answer to “calculate the middle-50-percent spread for six values.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.
A worked check
1–6 has IQR=5−2=3.
Where this model stops being reliable
Quartile conventions can differ for other sample sizes.
Learn it by changing one value
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Dictionary terms behind this calculator
Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.
These foundations help you understand why Interquartile range works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.
Hard requirements
- Reading formulas and substituting values
Interquartile range uses IQR=Q₃−Q₁. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.
Review this foundation about 4 min
Strong support
- Averages and representative values
Representative values help you judge what the Interquartile range inputs summarise and what the result can legitimately describe.
Review this foundation about 5 min
Optional enrichment
- Spread and measurement variation
Variation is not always part of the Interquartile range formula, but it helps you judge how stable a reported result may be.
Review this foundation about 6 min
Mathematics → algorithm → program
Implement this calculation in code
These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.
Algorithm
- Sort the six finite values.
- Use the second value as Q1 and the fifth as Q3.
- Subtract Q1 from Q3.
Python
def interquartile_range(*values: float) -> float:
ordered = sorted(values)
return ordered[4] - ordered[1]
assert interquartile_range(1,2,3,4,5,6) == 3
C
#include <assert.h>
void sort6(double x[6]){for(int i=5;i;i--)for(int j=0;j<i;j++)if(x[j]>x[j+1]){double t=x[j];x[j]=x[j+1];x[j+1]=t;}}
double interquartile_range(double a,double b,double c,double d,double e,double f){double x[6]={a,b,c,d,e,f};sort6(x);return x[4]-x[1];}
int main(void){assert(interquartile_range(1,2,3,4,5,6)==3);}
C++
#include <algorithm>
#include <array>
#include <cassert>
double interquartile_range(double a,double b,double c,double d,double e,double f){std::array<double,6>x{a,b,c,d,e,f};std::sort(x.begin(),x.end());return x[4]-x[1];}
int main(){assert(interquartile_range(1,2,3,4,5,6)==3);}
Linux x86-64 assembly
x86-64 NASM · System V ABI · Linux · double arguments and result in XMM registers
; double interquartile_range(double a,b,c,d,e,f)
global interquartile_range
section .text
interquartile_range:
sub rsp, 48
movsd [rsp], xmm0
movsd [rsp+8], xmm1
movsd [rsp+16], xmm2
movsd [rsp+24], xmm3
movsd [rsp+32], xmm4
movsd [rsp+40], xmm5
mov ecx, 5
.outer:
xor eax, eax
.inner:
movsd xmm0, [rsp+rax*8]
movsd xmm1, [rsp+rax*8+8]
ucomisd xmm0, xmm1
jbe .ordered
movsd [rsp+rax*8], xmm1
movsd [rsp+rax*8+8], xmm0
.ordered:
inc eax
cmp eax, ecx
jl .inner
dec ecx
jnz .outer
movsd xmm0, [rsp+32]
subsd xmm0, [rsp+8]
add rsp, 48
ret
MATLAB
function result = interquartile_range(v1, v2, v3, v4, v5, v6)
values = sort([v1, v2, v3, v4, v5, v6]);
result = values(5) - values(2);
end
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[v1_, v2_, v3_, v4_, v5_, v6_] := With[
{values = Sort[{v1, v2, v3, v4, v5, v6}]}, values[[5]] - values[[2]]
];
Continue in mathematical software
The downloaded file includes your current inputs and first calculated result. It is created locally.
Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Introductory Statistics 2e
Read the free OpenStax statistics textbookCite this book
- APA 7
- Illowsky, B., & Dean, S. (2023). Introductory statistics 2e. OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction
- MLA 9
- Illowsky, Barbara, and Susan Dean. Introductory Statistics 2e. OpenStax, 2023, https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
- Chicago author-date
- Illowsky, Barbara, and Susan Dean. 2023. Introductory Statistics 2e. Houston, TX: OpenStax. https://openstax.org/books/introductory-statistics-2e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Interquartile Range Calculator. MW SysArc Tools. https://math.mwsysarc.com/statistics/interquartile-range
MLA 9
MW SysArc. “Interquartile Range Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/statistics/interquartile-range. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Interquartile Range Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/statistics/interquartile-range.
Harvard
MW SysArc (2026) ‘Interquartile Range Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/statistics/interquartile-range (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_interquartile_range_six_2026,
author = {{MW SysArc}},
title = {Interquartile Range Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://math.mwsysarc.com/statistics/interquartile-range},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Interquartile Range Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://math.mwsysarc.com/statistics/interquartile-range
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Interquartile range do?
Calculate the middle-50-percent spread for six values.
How does the Interquartile range work?
The calculator applies IQR=Q₃−Q₁. The IQR measures central spread while reducing sensitivity to extremes.
What can I learn from the Interquartile range?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed . Calculations tested .