VAR

Statistical Functions

(4.8/5)

Calculates the sample variance of a set of numbers. Variance measures the average squared deviation from the mean. VAR uses the sample variance formula (n-1 denominator). Variance is the square of standard deviation. Essential for statistical analysis, measuring data variability, and understanding spread when working with sample data.

Interactive Formula Tester

Numbers:

Formula:

=VAR("10, 20, 30, 40, 50")

Complete Theory & Understanding

Master the fundamentals of Excel VAR function

Core Concept

The VAR function calculates the sample variance of a set of numbers. Variance measures the average squared deviation from the mean. VAR uses the sample variance formula with (n-1) denominator: Σ(xi - x̄)²/(n-1). Requires at least 2 values. Variance is the square of standard deviation: VAR = STDEV². VAR ≥ VARP always (for same data). Variance has squared units (not same scale as original data). Essential for statistical analysis, measuring data variability, understanding spread in samples, and calculating variance when working with sample data.

Why Use VAR?

Measure sample variability
Process variability in samples
Financial and business risk
Understanding sample spread

Key Characteristics

Sample Formula

Uses n-1 denominator

VAR uses sample formula

Squared Units

Variance has squared units

If data in meters, VAR in meters²

Minimum 2 Values

Requires at least 2 numbers

VAR needs spread to measure

VAR = STDEV²

Variance is squared STDEV

VAR(range) = STDEV(range)²

Function Anatomy

=VAR(parameters...)

Required

Parameters:

Function-specific parameters

Returns

Return Value:

Function-specific return type

Primary Use Cases

Statistical Analysis

Measure sample variability

Quality Control

Process variability in samples

Risk Assessment

Financial and business risk

Data Analysis

Understanding sample spread

Theory Summary

Precise

Exact matching required

Position-Based

Returns numeric position

Error-Safe

Handles missing text gracefully

Syntax & Parameters

=VAR(number1, number2)

Required

number1:

First number, cell reference, or range representing a sample.

Optional

number2:

Additional numbers, cell references, or ranges (up to 255 arguments).

Returns

Return Value:

The sample variance

Description: Returns the sample variance of a set of numbers

Interactive Examples

Basic VAR

Calculate sample variance

Input Text:

"10, 20, 30, 40, 50"

Formula:

=VAR(10, 20, 30, 40, 50)

Result:

250

Returns 250. Variance measures average squared deviation from mean. VAR uses sample formula: Σ(xi - x̄)²/(n-1).

VBA Implementation & Automation

Basic VAR in VBA

Use VAR function in VBA

' Basic VAR in VBA
Range("C1").Value = Application.WorksheetFunction.Var(Range("A1:A10"))
' Returns: Sample variance

' Calculate sample variance
Sub CalculateVAR()
    Dim varValue As Double
    varValue = Application.WorksheetFunction.Var(Range("A1:A10"))
    Range("B1").Value = varValue
End Sub

' Compare VAR with VARP
Sub CompareVARVARP()
    Dim varValue As Double
    Dim varpValue As Double
    varValue = Application.WorksheetFunction.Var(Range("A1:A10"))
    varpValue = Application.WorksheetFunction.VarP(Range("A1:A10"))
    Range("B1").Value = "VAR: " & varValue
    Range("B2").Value = "VARP: " & varpValue
    Range("B3").Value = "Difference: " & (varValue - varpValue)
End Sub

' Verify VAR = STDEV²
Sub VerifyVARFormula()
    Dim varValue As Double
    Dim stdevValue As Double
    varValue = Application.WorksheetFunction.Var(Range("A1:A10"))
    stdevValue = Application.WorksheetFunction.StDev(Range("A1:A10"))
    Range("B1").Value = "VAR: " & varValue
    Range("B2").Value = "STDEV²: " & (stdevValue * stdevValue)
    ' Should be equal (within rounding)
End Sub

' Statistical analysis with variance
Sub StatisticalAnalysis()
    Dim meanValue As Double
    Dim varValue As Double
    Dim stdevValue As Double
    meanValue = Application.WorksheetFunction.Average(Range("A1:A10"))
    varValue = Application.WorksheetFunction.Var(Range("A1:A10"))
    stdevValue = Application.WorksheetFunction.StDev(Range("A1:A10"))
    Range("B1").Value = "Mean: " & meanValue
    Range("B2").Value = "VAR: " & varValue
    Range("B3").Value = "STDEV: " & stdevValue
    Range("B4").Value = "STDEV²: " & (stdevValue * stdevValue)
End Sub

Business Applications

Statistical Analysis

Measure sample variability

=VAR(sample_data)

Quality Control

Process variability in samples

=VAR(process_sample)

Risk Assessment

Financial and business risk

=VAR(returns_sample)

Data Analysis

Understanding sample spread

=VAR(values)/AVERAGE(values)²

Common Issues & Solutions

#DIV/0! Error

VAR returns #DIV/0! with less than 2 values

=IF(COUNT(A1:A10)>=2, VAR(A1:A10), "Need 2+ values")

Solution: VAR requires at least 2 numeric values. With 0 or 1 value, it cannot calculate spread. Ensure you have at least 2 numeric values in the range.

VAR vs VARP Confusion

Uncertainty about which to use

VAR for samples, VARP for populations

Solution: VAR uses sample formula (n-1) - use for samples. VARP uses population formula (n) - use for entire populations. VAR ≥ VARP. For most samples, use VAR.

Squared Units

Variance has squared units

VAR has squared units, STDEV has original units

Solution: This is expected. Variance is in squared units. If data is in meters, variance is in meters². Use STDEV for original units (same scale as data).