Anomaly Formula: Percentage By Median

What it does:

This rule compares the latest value with the median of all previous values in your usage history. If the percentage difference from the median meets or exceeds your defined threshold, and the direction matches your selected change type, the rule triggers an anomaly alert.

When to use it:

Use this formula to detect meaningful changes relative to your typical usage, while reducing the effect of outliers. It’s ideal when your history includes occasional spikes or dips you want to ignore.

Mathematical Formula:

Let:

• L = Latest Value
• M = Median of historical values (excluding latest)
• T = Threshold (as a percentage)
• %Δ = Percentage Change
• %Δ = (|L − M| / M) × 100

Anomaly Condition:

%Δ ≥T

Direction Validation (based on Change Type):

• If Change Type = Increased, condition is valid only if L > M
• If Change Type = Decreased, condition is valid only if L < M
• If Change Type = Any, direction check is not required

Outcomes:

❌ Anomaly Detected → %Δ ≥ T and direction matches Change Type
☑️ Skipped → %Δ ≥ T, but direction does not match Change Type
✅ Normal → %Δ < T

Examples:

Example 1

Change Type: Increased
Threshold: 10%
History: 100, 105, 115

• If Latest Value = 112
  Result: Normal ✅
  Explanation:
    M = 105
    %Δ = (112 − 105) / 105 × 100 = 6.67%
    Percentage Change (6.67%) < Threshold (10%)

• If Latest Value = 120
  Result: Anomaly Detected ❌
  Explanation:
    M = 105
    %Δ = (120 − 105) / 105 × 100 = 14.29%
    Percentage Change (14.29%) ≥ Threshold (10%)

• If Latest Value = 90
  Result: Skipped ☑️
  Explanation:
    M = 105
    %Δ = |90 − 105| / 105 × 100 = 14.29%
    Percentage Change (14.29%) ≥ Threshold (10%)
    But direction = Decrease → does not match “Increased”

Example 2
Change Type: Decreased
Threshold: 15%
History: 250, 230, 260

• If Latest Value = 240
  Result: Normal ✅
  Explanation:
    M = 250
    %Δ = (250 − 240) / 250 × 100 = 4.00%
    Percentage Change (4.00%) < Threshold (15%)

• If Latest Value = 200
  Result: Anomaly Detected ❌
  Explanation:
    M = 250
    %Δ = (250 − 200) / 250 × 100 = 20%
    Percentage Change (20%) ≥ Threshold (15%)

• If Latest Value = 270
  Result: Skipped ☑️
  Explanation:
    M = 250
    %Δ = (270 − 250) / 250 × 100 = 8.00%
    Percentage Change (8.00%) < Threshold (15%)
    Also direction = Increase → does not match “Decreased”

Example 3
Change Type: Any
Threshold: 25%
History: 600, 660, 690

• If Latest Value = 700
  Result: Normal ✅
  Explanation:
    M = 660
    %Δ = (700 − 660) / 660 × 100 = 6.06%
    Percentage Change (6.06%) < Threshold (25%)

• If Latest Value = 850
  Result: Anomaly Detected ❌
  Explanation:
    M = 660
    %Δ = (850 − 660) / 660 × 100 = 28.79%
    Percentage Change (28.79%) ≥ Threshold (25%)