Calculation sequence
Step-by-step method
- Calculate the arithmetic mean.
- Sum squared deviations from the mean.
- Divide by n−1 for a sample and take the square root.
CommissioningIntermediateCross-Discipline Analysis
Standard Deviation Calculator
Calculate sample or population standard deviation for five entered readings.
Why it matters: Standard deviation quantifies spread but does not prove instrument accuracy, normality, or process stability.
Calculated result
Engineering evaluation
Sample standard deviation (s)1.581 selected units
- Arithmetic mean (Xbar)
- 11 selected units
- Sample variance (s²)
- 2.5 selected units squared
Engineering interpretation
Sample standard deviation is 1.581 selected units around a mean of 11. Standard deviation describes spread; it does not establish accuracy or a confidence interval by itself.
Engineering knowledge center
Understand the calculation—not just the answer
Governing relationships
Xbar = (X1+X2+X3+X4+X5)/5
s² = Σ(Xi−Xbar)²/(5−1)
s = √s²
Current substitution
Xbar = 11; sum of squared deviations = 10; s = 1.581.
Equation legend
Inputs and calculated quantities
- X1
- Reading 1 — same units
- X2
- Reading 2 — same units
- X3
- Reading 3 — same units
- X4
- Reading 4 — same units
- X5
- Reading 5 — same units
- s
- Sample standard deviation — selected units
- Xbar
- Arithmetic mean — selected units
- s²
- Sample variance — selected units squared
Applications
How this calculation is used
Building design
Summarize variability in repeated estimates.
Construction
Evaluate repeat readings or quality data.
Commissioning
Quantify repeatability and support uncertainty review.
Quality controls
Assumptions and limitations
Assumptions
- Entered values represent the same stable operating condition.
- Measurements and reference values use consistent units and boundaries.
Limitations
- This is a screening and field-verification tool, not an automatic acceptance decision.
- Project criteria, manufacturer data, governing standards, and measurement uncertainty remain controlling.
Field use
Verification procedure
- Confirm the approved reference values and test boundary.
- Stabilize the system and record calibrated field measurements.
- Review calculation assumptions, uncertainty, and supporting evidence before disposition.
Common engineering mistakes
- Comparing readings taken at different loads, modes, or reference conditions.
- Treating a calculated status as proof of code, contract, or manufacturer compliance.
Technical basis
References and source standards
- NIST/SEMATECH e-Handbook of Statistical MethodsPublished reference for averages, variability, standard deviation, calibration, and engineering data analysis.
- NIST Technical Note 1297Guidance for evaluating and expressing measurement uncertainty, including root-sum-square combination of independent standard uncertainty components.
Engineering calculation disclaimer
These engineering tools are provided for educational, preliminary evaluation, field verification, and commissioning support. Results depend on the accuracy of user-entered information and the assumptions stated for each calculation. Every colored status and comparison is a screening indicator only; project criteria, contract requirements, applicable codes, manufacturer instructions, measurement uncertainty, and authorized engineering judgment govern. The tools do not replace project-specific engineering analysis or the judgment of a licensed professional engineer.
Read the full use and limitation statement