Standard Deviation

The standard deviation (SD) measures how much values typically deviate from the mean.

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Sample SD: s = sqrt( Σ(xᵢ − x̄)² / (n − 1) )

In dentistry: SD helps interpret consistency—e.g., variation in probing depth reduction across patients after treatment.

Real Dental Scenario

Comparing pocket depth consistency between two clinics

Scenario: Two dental clinics measured periodontal pocket depths (mm) for 5 patients each. Which clinic shows more consistent treatment outcomes?

Clinic A (Consistent)

3.2 3.5 3.8 4.0 4.2

Clinic B (Variable)

2.0 3.0 4.5 5.5 7.0

1 Calculate the Means

2 Deviations from the Mean

Clinic A deviations

Clinic B deviations

3 Standard Deviation Results

Clinic A SD
-
Clinic B SD
-

4 Visual Comparison of Spread

Clinical Interpretation

Clinic A: Low SD (0.39 mm)

Consistent outcomes. Patients receive predictable treatment quality. Good for standardized protocols.

Clinic B: High SD (1.87 mm)

Highly variable outcomes. Some patients have shallow pockets (2.0), others have deep ones (7.0). Needs investigation.

Key Takeaway: The mean alone does not tell the full story. A small SD means reliable, consistent treatment results. A large SD signals inconsistency that may require clinical review.

Interactive: see SD change

Adjust the spread slider to generate different "pocket depth" samples and observe how SD affects the histogram.

0.20.82.5
1060200
Mean: -
SD: -
Interpretation: -

Histogram of measurements

Wider distributions reflect larger SD; tight clustering reflects small SD.

How to report SD (common patterns)