IQR = Q3 - Q1. Interquartile range — spread of the middle 50% of data. Robust to outliers.

What are Tukey fences?

Lower fence = Q1 - 1.5×IQR. Upper fence = Q3 + 1.5×IQR. Values outside are potential outliers.

Inclusive vs exclusive quartile method?

Inclusive: linear interpolation, (n-1) based. Exclusive: n-based. Can yield different Q1/Q3. State which you use.

How does it relate to box plots?

Box plot visualizes the five-number summary: whiskers to min/max, box from Q1 to Q3, line at median.

5 more

DESCRIPTIVEDescriptive StatisticsStatistics Calculator

📊

Five-Number Summary — Min, Q1, Median, Q3, Max

Summarize data with five key values. IQR, Tukey fences, range, outlier detection. Box plot visualization.

Concept Fundamentals

Min, Q1, Med, Q3, Max

Five Numbers

Distribution summary

Q3 − Q1

IQR

Interquartile range

< Q1−1.5·IQR

Outlier Rule

Tukey fence

Box-and-whisker plot

Application

Data visualization

Compute SummaryTukey EDA

Why This Statistical Analysis Matters

Why: Five-number summary gives a robust, compact view of center and spread. Preferred for skewed data. Foundation for box plots.

How: Enter data (comma/space separated). Choose quartile method (inclusive/exclusive). Get Min, Q1, Median, Q3, Max, IQR, fences, outliers.

●Min, Q1, Med, Q3, Max
●IQR = Q3 - Q1
●Fences for outliers

Sources:NIST Engineering Statistics HandbookWikipedia Five-Number Summary

📊

STATISTICSDescriptive Statistics

Five-Number Summary — Min, Q1, Median, Q3, Max

Summarize your data with five key values. IQR, fences, range, and visual box plot with outlier detection.

Quartile Calculator →IQR Calculator →

Real-World Scenarios — Click to Load

Data Input

Data — comma or space separated

Quartile method

five_number_summary.sh

CALCULATED

$ five_number_summary --n=10 --method="inclusive"

Min

65.0000

73.5000

Median

84.5000

89.5000

Max

95.0000

IQR

16.0000

Range

30.0000

Fences

[49.50, 113.50]

Outliers

None

Five Number Summary

Min, Q1, Median, Q3, Max

IQR = 16.000

Min: 65Q1: 73.50Median: 84.50Q3: 89.50Max: 95

numbervibe.com/calculators/statistics/five-number-summary-calculator

Box Plot — Five-Number Summary

Box spans Q1–Q3; median line inside. Outliers shown as red points.

Five Values Comparison

Data Strip Chart

Calculation Breakdown

FIVE-NUMBER SUMMARY

Min

65.0000

ext{First} ext{value} ext{after} ext{sorting}

Q1 (25th percentile)

73.5000

Method: inclusive

Median (Q2)

84.5000

50th ext{percentile}

Q3 (75th percentile)

89.5000

Method: inclusive

SPREAD & FENCES

Max

95.0000

ext{Last} ext{value} ext{after} ext{sorting}

IQR

16.0000

Q3 − Q1 = 89.50 − 73.50

Lower fence

49.5000

Q1 − 1.5×IQR = 73.50 − 24.00

Upper fence

113.5000

Q3 + 1.5×IQR = 89.50 + 24.00

Range

30.0000

Max − Min = 95 − 65

Outliers

None

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

📈 Statistical Insights

IQR

IQR = Q3 - Q1 — middle 50% spread

— Tukey

1.5×IQR

Tukey fence multiplier for outliers

— EDA

Five key values summarize distribution

— Definition

Key Takeaways

• The five-number summary consists of Min, Q1 (25th percentile), Median (Q2), Q3 (75th percentile), and Max
• IQR = Q3 − Q1 measures the spread of the middle 50% of the data
• Lower fence = Q1 − 1.5×IQR; Upper fence = Q3 + 1.5×IQR — values outside are potential outliers
• Range = Max − Min gives the total spread of the dataset
• Quartile method (inclusive vs exclusive) affects Q1 and Q3 values — choose based on your analysis needs
• The box plot visualizes the five-number summary: box spans Q1–Q3, line inside is median

Did You Know?

📊John Tukey introduced the five-number summary in his 1977 book "Exploratory Data Analysis".Source: Tukey, 1977

📐The box in a box plot spans from Q1 to Q3 — it contains exactly 50% of the data.Source: NIST Handbook

🔍The 1.5×IQR rule is a convention; some analysts use 2×IQR or 3×IQR for stricter outlier detection.Source: Wolfram MathWorld

📈Five-number summaries are robust: they resist the influence of extreme values better than mean and standard deviation.Source: Khan Academy

🧪Different software uses different quartile formulas — Excel, R, and Python can give slightly different Q1/Q3 values.Source: Wikipedia

📉Comparing five-number summaries across groups quickly reveals differences in center, spread, and skewness.Source: NIST Handbook

How It Works

1. Sort the Data

Arrange all values in ascending order. Min is the first value; Max is the last.

2. Compute Quartiles

Q1 = 25th percentile, Median = 50th percentile, Q3 = 75th percentile. Use linear interpolation between adjacent values.

3. Calculate IQR and Fences

IQR = Q3 − Q1. Lower fence = Q1 − 1.5×IQR, Upper fence = Q3 + 1.5×IQR.

4. Identify Outliers

Any value below the lower fence or above the upper fence is flagged as a potential outlier.

5. Visualize with Box Plot

The box spans Q1 to Q3; the line inside is the median. Whiskers extend to min/max within fences; outliers are plotted as points.

Expert Tips

Quartile Method

Inclusive (default) matches Excel and many tools. Exclusive matches R type 7. State your choice in reports.

Outlier Handling

Don't remove outliers blindly. Investigate whether they are data errors or genuine extreme values.

Sample Size

Five-number summary works best with n ≥ 5. For very small samples, consider a strip plot instead.

Comparing Groups

Place five-number summaries side-by-side to compare center (median), spread (IQR), and skewness across groups.

Why Use This Calculator vs Other Tools?

Feature	This Calculator	Excel	R	Python
Five-number summary	✅	⚠️ Multiple functions	✅	✅
Box plot + strip chart	✅	⚠️ Manual	✅	✅
Quartile method choice	✅	❌	✅	⚠️
Outlier list + fences	✅	❌	⚠️	⚠️
Educational content	✅	❌	❌	❌
Copy & share results	✅	❌	❌	❌
AI-powered interpretation	✅	❌	❌	❌
No installation required	✅	✅	❌	❌