Interquartile Range Calculator
Calculate IQR with Step-by-Step Derivation
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Interquartile Range Formula
IQR = Q3 - Q1
Lower Fence = Q1 - 1.5 × IQR
Upper Fence = Q3 + 1.5 × IQR
Outliers: values outside [Lower Fence, Upper Fence]
IQR measures the spread of the middle 50% of data and is resistant to outliers. Used in box plots.
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At least 4 values required. IQR uses Tukey method for quartile calculation.
What is Interquartile Range?
The interquartile range (IQR) is the range of the middle 50% of data. It is calculated as Q3 - Q1 and is resistant to extreme values.
Quartiles
Q1=25%, Q2=50% (median), Q3=75% percentiles
IQR Calculation
IQR = Q3 - Q1, the range of the middle half of data
Outlier Fences
1.5×IQR rule: lower=Q1-1.5IQR, upper=Q3+1.5IQR
Resistant Measure
IQR is not affected by outliers like range or standard deviation
💡 Example: Data: 10,12,15,18,20,22,25,28,30,35. Q1=15, Q2=21, Q3=28, IQR=13.
Applications
Descriptive Statistics
Data Analysis
Box Plots
Outlier Detection
Quality Control
Frequently Asked Questions
What is interquartile range (IQR)?▼
IQR = Q3 - Q1. It measures the spread of the middle 50% of data. IQR is resistant to outliers and used in box plots and outlier detection.
How is IQR calculated?▼
First find Q1 (25th percentile) and Q3 (75th percentile). Then IQR = Q3 - Q1. This represents the range containing the middle half of the data.
What are outlier fences?▼
Lower fence = Q1 - 1.5×IQR. Upper fence = Q3 + 1.5×IQR. Values outside these fences are considered outliers.
Why is IQR important?▼
IQR describes data spread without being affected by extreme values. It is used in descriptive statistics, box plots, and identifying outliers.
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