Outlier Detection Calculator Formula

Understand the math behind the outlier detection calculator. Each variable explained with a worked example.

Use the Outlier Detection Calculator

Formulas Used

IQR

iqr_val = iqr

Lower Fence

lower_fence = q1 - 1.5 * iqr

Upper Fence

upper_fence = q3 + 1.5 * iqr

Outside Fences? (1=yes)

is_outlier = ((value < (q1 - 1.5 * iqr)) + (value > (q3 + 1.5 * iqr))) > 0 ? 1 : 0

Distance Beyond Fence

distance = abs(value) > abs(q3 + 1.5 * iqr) ? abs(value - (q3 + 1.5 * iqr)) : abs(value) < abs(q1 - 1.5 * iqr) ? abs(value - (q1 - 1.5 * iqr)) : 0

Variables

VariableDescriptionDefault
valueValue to Test95
q1Q1 (25th Percentile)30
q3Q3 (75th Percentile)70
iqrDerived value= q3 - q1calculated

How It Works

How to Detect Outliers Using the IQR Method

Formula

IQR = Q3 - Q1

Lower Fence = Q1 - 1.5 * IQR

Upper Fence = Q3 + 1.5 * IQR

Values below the lower fence or above the upper fence are flagged as potential outliers. The 1.5 multiplier is Tukey's convention. Using 3.0 instead identifies extreme outliers.

Worked Example

Q1 = 30, Q3 = 70. Is 95 an outlier?

value = 95q1 = 30q3 = 70
  1. 01IQR = 70 - 30 = 40
  2. 02Lower fence = 30 - 1.5*40 = 30 - 60 = -30
  3. 03Upper fence = 70 + 1.5*40 = 70 + 60 = 130
  4. 0495 is between -30 and 130, so it is NOT an outlier
  5. 05It would need to exceed 130 to be flagged

Ready to run the numbers?

Open Outlier Detection Calculator