How to Calculate Variance: A Comprehensive Step-by-Step Guide with Examples and Tools

Last Modified: January 28, 2025 - 7 min read

Julian Alvarado
calculate variance

Variance is a fundamental concept in statistics that helps us understand how data points spread out from their average. Whether you’re a student, researcher, or professional working with data, knowing how to calculate and interpret variance is crucial. This guide will walk you through the process, providing clear explanations, practical examples, and useful tools to make variance calculation a breeze.

Types of Variance Functions in Google Sheets

Google Sheets offers two main variance functions:

Population Variance: VAR.P()

Use VAR.P() when you have data for an entire population. The syntax is:

=VAR.P(number1, [number2, …])

Sample Variance: VAR.S()

Use VAR.S() when working with a sample of a larger population. The syntax is:

=VAR.S(number1, [number2, …])

Calculating Variance in Google Sheets: Step-by-Step Guide

Let’s walk through the process of calculating variance using Google Sheets functions.

Step 1: Prepare Your Data

First, enter your data into a Google Sheets column. For example:

AB
Data
10
15
20
25
30

Step 2: Use the Built-in Variance Functions

Google Sheets provides easy-to-use functions for both population and sample variance.

Population Variance

To calculate population variance, use the VAR.P() function:

  1. Click an empty cell (e.g., B1)
  2. Type =VAR.P(
Enter data into Google Sheets.
  1. Select your data range (e.g., A2:A6)
Using the var.p() function to calculate population variance
  1. Close the parenthesis and press Enter

Your formula should look like this:

=VAR.P(A2:A6)

Sample Variance

For sample variance, use the VAR.S() function:

  1. Click an empty cell (e.g., B2)
  2. Type =VAR.S(
 use the var() function to calculate the sample variance
  1. Select your data range (e.g., A2:A6)
Select the range to calculate the sample variance.
  1. Close the parenthesis and press Enter
Close the parentheses and press Enter.

Your formula should look like this:

=VAR.S(A2:A6)

After applying these formulas, your sheet might look like this:

AB
DataVariance
1050 (Population)
1562.5 (Sample)
20
25
30

Step 3: Interpret the Results

The results in cells B1 and B2 represent the population and sample variance, respectively. A larger value indicates greater data spread, while a smaller value suggests data points are closer to the mean.

Manual Calculation in Google Sheets

For educational purposes or to understand the process better, you can calculate variance manually in Google Sheets:

  1. Calculate the mean: In cell C1, enter: =AVERAGE(A2:A6)
Calculating the mean using the average function
  1. Calculate deviations from the mean: In cell B2, enter: =A2-$C$1 Drag the formula down to B6
Calculate the deviations from the mean.
  1. Square the deviations: In cell C2, enter: =B2^2 Drag the formula down to C6
And cell C2, enter the formula and drag down.
  1. Sum the squared deviations: In cell D1, enter: =SUM(C2:C6)
SLD1 entered this formula.
  1. Divide by n or n-1: For population variance (in E1): =D1/COUNT(A2:A6) For sample variance (in E2): =D1/(COUNT(A2:A6)-1)
For sample variance (in E2): =D1/(COUNT(A2:A6)-1)
Image6

Your sheet might now look like this:

ABCDE
DataDeviationSquared DevSumVariance
10-1010025050 (Population)
15-52562.5 (Sample)
2000
25525
3010100

Practical Examples in Google Sheets

Let’s look at some real-world examples of calculating variance in Google Sheets.

Example 1: Stock Price Volatility

Suppose you’re analyzing the closing prices of a stock over 10 days:

AB
DateClosing Price
1-Jun100
2-Jun102
3-Jun98
4-Jun103
5-Jun99
6-Jun101
7-Jun97
8-Jun104
9-Jun100
10-Jun102

To calculate sample variance: In cell C1, enter: =VAR.S(B2:B11)

 In cell C2, enter: =VAR.P(B2:B11)

To calculate population variance: In cell C2, enter: =VAR.P(B2:B11)

Pressing Enter, and the answer being 4.4.

The results should be approximately 4.93 (sample) and 4.44 (population).

Example 2: Manufacturing Quality Control

A factory produces widgets with a target weight of 50 grams. To check consistency, they weigh 12 randomly selected widgets:

AB
WidgetWeight (g)
149.8
250.2
350.0
450.1
549.9
650.3
749.7
850.2
950.0
1049.8
1150.1
1250.0

Calculate sample variance: In cell C1, enter: =VAR.S(B2:B13)

The result should be approximately 0.0336, suggesting a consistent manufacturing process.

The result should be approximately 0.0336, suggesting a consistent manufacturing process.

Advanced Variance Techniques in Google Sheets

Using ARRAYFORMULA for Efficient Calculations

When dealing with large datasets, you can use ARRAYFORMULA to calculate variance for multiple ranges simultaneously:

=ARRAYFORMULA(VAR.S(A1:A100, B1:B100, C1:C100))

This formula calculates the sample variance for each column (A, B, and C) in one go.

Creating a Dynamic Variance Dashboard

You can build a dynamic variance dashboard in Google Sheets:

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  1. Create a dropdown menu for selecting data ranges: In cell A1, go to Data > Data validation and set up a list of options
  2. Use INDIRECT and INDEX functions to make your variance calculations dynamic: In cell B1, enter: =VAR.S(INDIRECT(A1))

This setup allows you to quickly switch between different data ranges and see the variance update automatically.

Variance Analysis with Pivot Tables

Pivot tables can help analyze variance across multiple dimensions:

  1. Select your data range
  2. Go to Insert > Pivot table
Insert chart pivot table.
  1. Add relevant fields to rows and columns
Greetings, The Pivot Table.
  1. In the Values section, add your numeric field and change the summarize by option to “Variance
Adding the numeric field and changing the summarize by option to.

This method allows you to quickly compare variances across different categories or time periods.

Demystifying Variance: What It Is and Why It Matters

Variance is a statistical measure that quantifies the spread of data points around their mean (average). It tells us how much our data deviates from the expected value. In simpler terms, variance helps us understand if our data points are tightly clustered or widely scattered.

The Significance of Variance

Why should we care about variance? Here are a few key reasons:

  1. Data distribution insights: Variance provides valuable information about how data is distributed, which is crucial for many statistical analyses.
  2. Risk assessment: In finance, variance helps measure the volatility of investments, aiding in risk management.
  3. Quality control: Manufacturing processes use variance to monitor product consistency and identify potential issues.
  4. Research reliability: Scientists use variance to evaluate the reliability of their experimental results.

Variance vs. Standard Deviation: Two Sides of the Same Coin

While variance and standard deviation are closely related, they serve different purposes:

  • Variance is expressed in squared units of the original data, making it less intuitive to interpret.
  • Standard deviation is the square root of variance, expressed in the same units as the original data, making it easier to understand in practical terms.

Both measures provide information about data spread, but standard deviation is often preferred for its interpretability.

Exploring Types of Variance: Population vs. Sample

Population Variance: The Complete Picture

Population variance applies when you have data for an entire population. It’s used when you have access to every possible data point in a dataset.

Key characteristics:

  • Uses the symbol σ² (sigma squared)
  • Divides by N (total number of data points)
  • Provides a complete picture of data variability

Sample Variance: Making Inferences from a Subset

Sample variance is used when you have a subset of data from a larger population. It’s commonly used in real-world scenarios where collecting data from an entire population is impractical or impossible.

Key characteristics:

  • Uses the symbol s²
  • Divides by n-1 (number of data points minus one)
  • Provides an estimate of population variance
  • Accounts for sampling error

Choosing the Right Type: When to Use Each Variance

The choice between population and sample variance depends on your data and research goals:

  • Use population variance when you have complete data for a finite population.
  • Use sample variance when you’re working with a sample to make inferences about a larger population.

In most real-world scenarios, you’ll likely use sample variance, as it’s rare to have access to an entire population’s data.

Wrapping Up: Key Takeaways and Next Steps

Understanding how to calculate and interpret variance is a valuable skill in data analysis. Here’s a quick recap of what we’ve covered:

  1. Variance measures the spread of data points around their mean.
  2. There are two types of variance: population and sample.
  3. Calculating variance involves five main steps: finding the mean, calculating deviations, squaring deviations, summing squared deviations, and dividing by N or N-1.
  4. Various tools, from Excel to specialized statistical software, can help simplify variance calculations.
  5. Variance has important applications in finance, quality control, scientific research, and many other fields.

As you continue to work with data, remember that variance is just one tool in the statistical toolbox. To deepen your understanding of data analysis, consider exploring related concepts like standard deviation, correlation, and regression analysis.

Ready to put your new knowledge into practice? Try calculating the variance of a dataset relevant to your field or interests. The more you work with these concepts, the more comfortable and proficient you’ll become.

For more advanced data analysis tools and techniques, check out Coefficient. Our platform offers powerful solutions to help you extract meaningful insights from your data and make informed decisions.

Meta Title: Master Variance Calculation: Step-by-Step Guide with Examples

Meta Description: Learn how to calculate variance with our comprehensive guide. Understand formulas, see real-world examples, and discover tools to simplify your statistical analysis.

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Julian Alvarado Content Marketing
Julian is a dynamic B2B marketer with 8+ years of experience creating full-funnel marketing journeys, leveraging an analytical background in biological sciences to examine customer needs.
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