STATISTICSDescriptive StatisticsStatistics Calculator
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Range Calculator

Free range calculator. Range, semi-range, IQR, interdecile range, interpercentile range, relative ra

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Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

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STATISTICSDescriptive Statistics

Range, IQR, Interdecile Range, Relative Range

Compute range, semi-range, IQR, interdecile range, interpercentile range, relative range, coefficient of range, and range rule of SD.

IQR Calculator โ†’Dispersion โ†’

Real-World Scenarios โ€” Click to Load

Data & Percentile Bounds

range_results.sh
CALCULATED
$ range_calc --n=15 --p_low=5 --p_high=95
Range
43.0000
IQR
17.5000
Interdecile Range
31.2000
Relative Range
53.04%
Semi-Range
76.5000
Coeff. of Range
0.2810
Range Rule SD
10.7500
Min / Max
55.00 / 98.00
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Range Calculator Result
n = 15
Range = 43.000
IQR = 17.500IDR = 31.200Rel.Range = 53.0%
numbervibe.com/calculators/statistics/range-calculator

Data Strip with Range/IQR/IDR Highlighted

Red: below D1 or above D9; Amber: D1โ€“Q1 or Q3โ€“D9; Blue: Q1โ€“Q3 (IQR).

Range Measures Comparison

Key Measures Overview

Calculation Breakdown

DATA
Min
55.0000
Smallest value in sorted data
Max
98.0000
Largest value in sorted data
RANGE MEASURES
Range
43.0000
Max โˆ’ Min = 98.00 โˆ’ 55.00
Semi-Range (Midrange)
76.5000
(Max + Min) / 2 = (98.00 + 55.00) / 2
IQR
17.5000
Q3 โˆ’ Q1 = 91.00 โˆ’ 73.50
Interdecile Range
31.2000
D9 โˆ’ D1 = 95.60 โˆ’ 64.40
Interpercentile (P5โ€“P95)
36.7000
P95 โˆ’ P5
RELATIVE MEASURES
Relative Range
53.04%
(Range / Mean) ร— 100 = (43.00 / 81.07) ร— 100
Coefficient of Range
0.2810
(Max โˆ’ Min) / (Max + Min)
ESTIMATION
Range Rule SD
10.7500
Range / 4 โ‰ˆ ฯƒ for normal data

For educational and informational purposes only. Verify with a qualified professional.

Key Takeaways

  • โ€ข Range = Max โˆ’ Min โ€” simplest measure of spread, sensitive to outliers
  • โ€ข Semi-Range (Midrange) = (Max + Min) / 2 โ€” midpoint of the range
  • โ€ข IQR = Q3 โˆ’ Q1 โ€” spread of middle 50%, robust to outliers
  • โ€ข Interdecile Range = D9 โˆ’ D1 โ€” spread of middle 80%, more robust than range
  • โ€ข Relative Range = (Range / Mean) ร— 100% โ€” scale-invariant, like CV but for range
  • โ€ข Coefficient of Range = (Max โˆ’ Min) / (Max + Min) โ€” dimensionless [0, 1]
  • โ€ข Range Rule of SD: ฯƒ โ‰ˆ Range / 4 โ€” rough estimate for normal data

Did You Know?

๐Ÿ“ŠRange is the simplest measure of dispersion but is highly sensitive to outliers. One extreme value can dramatically inflate it.Source: NIST Handbook
๐Ÿ“IQR and Interdecile Range are robust โ€” they resist the influence of extreme values. Use them for skewed data.Source: Wolfram MathWorld
๐Ÿ”The midrange is the midpoint of the range โ€” useful for symmetric distributions and quick center estimates.Source: Khan Academy
๐Ÿ“ˆRelative Range = Range/Mean ร— 100% โ€” like CV but for range instead of SD. Compare spread across different scales.Source: Statistics texts
๐ŸงชFor grouped data: Range = upper boundary of last class โˆ’ lower boundary of first class.Source: Descriptive statistics
๐Ÿ“‰Coefficient of Range โˆˆ [0, 1]. Zero when all values are equal; approaches 1 when data spans a wide range.Source: Mathematical properties

Expert Tips

When to Use Range

Use range for quick summaries. Prefer IQR or interdecile when outliers exist.

Custom Percentiles

Set P5โ€“P95 for middle 90%, or P10โ€“P90 for middle 80%. Customize to your needs.

Coefficient of Range

Dimensionless; compare spread across datasets with different units or scales.

Range Rule

ฯƒ โ‰ˆ Range/4 works best for normal data with n > 15. Rough estimate only.

Range Measures Comparison

MeasureFormulaRobustnessUse Case
RangeMax โˆ’ MinLow (sensitive to outliers)Quick summary
Semi-Range(Max + Min) / 2LowCenter of range
IQRQ3 โˆ’ Q1HighMiddle 50% spread
InterdecileD9 โˆ’ D1HighMiddle 80% spread
Coefficient(Maxโˆ’Min)/(Max+Min)LowCompare across scales

Frequently Asked Questions

Why is range sensitive to outliers?

Range uses only Min and Max. One extreme value can dramatically increase the range.

What is the interdecile range?

D9 โˆ’ D1. Middle 80% of data. More robust than range when extremes exist.

When to use IQR vs range?

Use IQR for skewed data or when outliers exist. Range is fine for quick summaries of clean data.

What is the coefficient of range?

(Maxโˆ’Min)/(Max+Min). Dimensionless; range [0,1]. Useful for comparing across scales.

What is the range rule of SD?

ฯƒ โ‰ˆ Range/4. Rough estimate for normal data. Useful when n is large and SD is unavailable.

What is relative range?

Range/Mean ร— 100%. Scale-invariant; like CV but for range.

How do I interpret the data strip chart?

Red = below D1 or above D9 (outer 20%); Amber = D1โ€“Q1 or Q3โ€“D9; Blue = Q1โ€“Q3 (IQR, middle 50%).

Can I use custom percentiles?

Yes. Set lower and upper percentiles (e.g., 5 and 95) for interpercentile range of middle 90%.

Range by the Numbers

50%
Data in IQR
80%
Data in IDR
ยผ
Range Rule
4
Key measures

Formulas Reference

Range = Max โˆ’ Min

Semi-Range (Midrange) = (Max + Min) / 2

IQR = Q3 โˆ’ Q1

Interdecile Range = D9 โˆ’ D1

Relative Range = (Range / Mean) ร— 100%

Coefficient of Range = (Max โˆ’ Min) / (Max + Min)

Range Rule of SD: ฯƒ โ‰ˆ Range / 4

Rough estimate for normal data

Applications

Quality Control

Range and IQR monitor process variation. Coefficient of range compares across products.

Finance

Stock price ranges, volatility. Interdecile range for robust return analysis.

Healthcare

Lab value ranges. IQR for robust reference intervals.

Education

Score ranges, grade distributions. IQR for robust spread comparisons.

Disclaimer: Range is sensitive to outliers. For skewed data, prefer IQR or interdecile range. Range rule of SD is a rough estimate only.

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