Lower Fence Calculator

Calculate lower fence for outlier detection using quartiles and IQR

Enter Your Data

Higher values make outlier detection less strict

Note: At least 4 data points are required to calculate quartiles and fences. Currently you have 0 valid numbers.

Example: Simple Dataset

Data: 1, 2, 3, 4, 5

Q1: 2

Q3: 4

IQR: 4 - 2 = 2

Lower Fence Calculation

Lower Fence = Q1 - 1.5 × IQR

Lower Fence = 2 - 1.5 × 2 = -1

Result: -1

1.5 IQR Rule

Standard method for outlier detection

Values below Q1 - 1.5×IQR are outliers

Values above Q3 + 1.5×IQR are outliers

Adjustable multiplier for different sensitivities

Understanding Lower Fence and Outlier Detection

What is the Lower Fence?

The lower fence is a statistical boundary used to identify outliers in a dataset. Any data point below the lower fence is considered an outlier - an unusually small value that deviates significantly from the rest of the data.

How it Works

  1. Find the first quartile (Q1) and third quartile (Q3)
  2. Calculate the interquartile range (IQR = Q3 - Q1)
  3. Apply the formula: Lower Fence = Q1 - k × IQR
  4. Identify outliers below the lower fence

Lower Fence Formula

Lower Fence = Q1 - k × IQR

where k is typically 1.5 (standard) or 2-3 (more lenient)

Multiplier Guidelines

  • k = 1.5: Standard rule, moderate outlier detection
  • k = 2.0: More conservative, fewer outliers
  • k = 3.0: Very conservative, only extreme outliers

Applications and Uses

Quality Control

Identify defective products or unusual measurements in manufacturing

Data Cleaning

Remove or flag suspicious data points before analysis

Statistical Analysis

Ensure robust statistical models by handling outliers appropriately