VAR.S & VAR.P Statistical Variance Formulas
Learn variance calculations in Excel with VAR.S and VAR.P. Understand squared dispersion units, sample Bessel correction, and links to standard deviation cleanly.
VAR.S & VAR.P Statistical Formulas
When financial analysts model investment risk or data scientists build regression ANOVA tables, the primary foundational metric they compute is variance. Variance measures the average squared difference between each data point and the dataset's mean.
Before you can compute covariance, correlation, or standard deviation, variance is the mathematical engine running under the hood. However, variance has two traits that often confuse spreadsheet users: its units are squared (e.g. dollars squared or percent squared), and Excel offers both VAR.S (Sample) and VAR.P (Population) variants.
This guide explains how variance works, clarifies the connection between variance and standard deviation, and shows when to use each formula.
VAR.S (Sample - N - 1)
Divides the sum of squared differences by N - 1. Standard in finance, quality audits, and scientific experiments.
VAR.P (Population - N)
Divides by total count N. Used strictly when data encompasses 100% of the entire population with zero sampling.
Quick Comparison: Variance vs Standard Deviation
| Metric | Formula Syntax | Measurement Unit | Mathematical Relationship |
|---|---|---|---|
| Sample Variance | =VAR.S(range) | Squared units (e.g. %² or $²) | Base dispersion metric (s²) |
| Sample Standard Deviation | =STDEV.S(range) | Original units (e.g. % or $) | =SQRT(VAR.S(range)) |
| Population Variance | =VAR.P(range) | Squared units (e.g. %² or $²) | Base population dispersion (σ²) |
How the Variance Engines Work
1. Mathematical Link to Standard Deviation
Standard deviation is simply the square root of variance:
STDEV.S = SQRT(VAR.S)
Variance = STDEV ^ 2Because variance squares the differences from the mean, it penalizes large outliers much more heavily than small ones.
2. The Sample vs Population Selection Rule
- Use VAR.S for almost all business cases where you evaluate a historical sample of monthly returns, a batch of manufactured parts, or a customer survey.
- Use VAR.P only when the dataset contains every single entity in existence (such as entire company headcounts or closed census records).
3. Skipping Text and Empty Cells
Both VAR.S and VAR.P automatically skip blank cells and text labels without throwing errors.
Real-Life Workplace Scenarios
1. Portfolio Risk Modeling
Quantitative analysts evaluate asset return variance as the core input into modern portfolio theory and Sharpe ratio models.
2. ANOVA (Analysis of Variance) Testing
Operations teams compare variance across different production shifts to verify whether changes in tooling significantly altered consistency.
Common Mistakes to Avoid
- Misinterpreting Squared Units: If your input is in dollars ($), the variance output is in dollars squared ($²). Do not confuse this with dollar amounts—take the square root to return to dollars.
- Using Legacy VAR: The old
VARfunction is kept only for backwards compatibility. UseVAR.Sfor modern sheets.
Audit monthly return variance in our spreadsheet playground below.
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