STATISTICSDescriptive StatisticsStatistics Calculator
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Upper and Lower Fence Calculator

Free upper and lower fence calculator. IQR, inner/outer fences, custom multiplier. Box plot, data st

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Why This Statistical Analysis Matters

Why: Statistical calculator for analysis.

How: Enter inputs and compute results.

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STATISTICSDescriptive Statistics

Inner/Outer Fences โ€” Outlier Boundaries

Compute inner and outer fences using IQR with customizable multiplier. Box plot with fences. Data strip colored by zone (green/yellow/red).

Outlier Calculator โ†’IQR Calculator โ†’

Real-World Scenarios โ€” Click to Load

Data โ€” comma or space separated

fence_results.sh
CALCULATED
$ fence --k_inner=1.5 --k_outer=3 --n=12
Q1
79.5000
Q3
92.7500
IQR
13.2500
Inner fences
[59.63, 112.63]
Outer fences
[39.75, 132.50]
Inliers
12
Mild outliers
0
Extreme outliers
0
Share:
Fence Result
n = 12 values
Inner: [59.6, 112.6]
Outer: [39.8, 132.5]Inliers: 12Mild: 0 | Extreme: 0
numbervibe.com/calculators/statistics/upper-lower-fence-calculator

Box Plot with Inner/Outer Fences

Outer LInner LInner UOuter U

Amber = inner fences (k=1.5); Red dashed = outer fences (k=3). Yellow = mild; Red = extreme.

Data Strip by Zone

Green = inlier | Yellow = mild outlier | Red = extreme outlier

Fence Boundaries (Lower Outer โ†’ Upper Outer)

Calculation Breakdown

QUARTILES
Q1
79.5000
25th ext{percentile}
Q3
92.7500
75th ext{percentile}
IQR
13.2500
Q3 โˆ’ Q1 = 92.75 โˆ’ 79.50
INNER FENCES
Lower inner fence
59.6250
Q1 โˆ’ 1.5ร—IQR
Upper inner fence
112.6250
Q3 + 1.5ร—IQR
OUTER FENCES
Lower outer fence
39.7500
Q1 โˆ’ 3ร—IQR
Upper outer fence
132.5000
Q3 + 3ร—IQR
Inliers
12
ext{Between} ext{inner} ext{fences}
Mild outliers
0
ext{Between} ext{inner} ext{and} ext{outer}
Extreme outliers
0
ext{Beyond} ext{outer} ext{fences}

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

Key Takeaways

  • Q1 = 25th percentile, Q3 = 75th percentile; IQR = Q3 โˆ’ Q1
  • Inner fences (default k=1.5): Lower = Q1 โˆ’ kร—IQR, Upper = Q3 + kร—IQR
  • Outer fences (default k=3.0): Lower = Q1 โˆ’ 3ร—IQR, Upper = Q3 + 3ร—IQR
  • Mild outliers: between inner and outer fences; Extreme: beyond outer fences
  • Inliers: between inner fences. Adjacent values = whisker endpoints

Did You Know?

๐Ÿ“ŠJohn Tukey introduced the 1.5ร—IQR rule in his 1977 book "Exploratory Data Analysis"Source: Tukey EDA
๐Ÿ“Custom multiplier k lets you tune sensitivity โ€” smaller k flags more outliersSource: NIST Handbook
๐Ÿ”Adjacent values are the min/max data points within the inner fences โ€” whisker endpointsSource: Box plot convention

Frequently Asked Questions

What is the difference between inner and outer fences?

Inner fences (1.5ร—IQR) flag mild outliers. Outer fences (3ร—IQR) flag extreme outliers. Values between inner and outer = mild; beyond outer = extreme.

Can I use a custom multiplier?

Yes. This calculator lets you set k for inner and outer fences. Default 1.5 and 3.0 are Tukey's standard. Use smaller k for stricter detection.

What are adjacent values?

Lower adjacent = smallest data point โ‰ฅ lower inner fence. Upper adjacent = largest โ‰ค upper inner fence. These are the whisker endpoints in a box plot.

Disclaimer: Fences are heuristic rules. Custom k changes sensitivity. For publication, state your k and quartile method. Investigate outliers before removing.

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