Pooled variance calculator
Welcome to our userfriendly Pooled Variance Calculator. This tool rapidly and accurately calculates the pooled variance (s²p) from your data. Whether you're a student, researcher, or statistician, our calculator offers a complete solution with a single click.
What is Pooled Variance?
Pooled variance is a statistical method that estimates the variance of many populations whose means are anticipated to be equal. It is often used in ttests and ANOVA to compare the means of two or more groups.
How to Calculate Pooled Variance
To calculate pooled variance, we need the sample sizes and standard deviations of our data sets. The formula for pooled variance is:
\( \mathrm{s_{p}^{2} =\frac{(n_{1}1)\times s_{1}^{2}+(n_{2}1)\times s_{2}^{2}}{n_{1}+n_{2}2}} \)
where:
 \(\mathrm{n_{1}}\) and \(\mathrm{n_{2}}\) are the sample sizes.
 \(\mathrm{s_{1}}\) and \(\mathrm{s_{2}}\) are the sample standard deviation.
Using Our Pooled Variance Calculator
Our calculator allows you to input your data directly or provide a data set. Here's how it works:
 Select Data Type: Choose whether you want to enter data directly or provide a data set.

Enter Values: Depending on your selection, input the necessary values:
 Direct Input: Enter the sample sizes and standard deviations.
 Data Provided: Enter the individual data points for each sample.
 Calculate: Click the "Calculate" button to get your results.
Features of Our Calculator
Easy to navigate and input your data.
Provides a stepbystep breakdown of the calculations.
Round results to your desired number of decimal places.
Example Calculation
Let's say you have two samples:
Sample \(1\) : \(\mathrm{n_{1}} = 10\), \(\mathrm{s_{1} =3.2 }\)
Sample \(2\) : \(\mathrm{n_{2}} = 15\), \(\mathrm{s_{2} =6.2 }\)
Using our calculator, you would enter these values, and it will compute the pooled variance for you.
Why Use our Pooled Variance Calculator ?
Pooled variance is critical when performing hypothesis tests on two or more samples. It delivers a more accurate variance estimate by merging data from all samples, particularly when sample sizes are different.
FAQs
Q: What is pooled variance used for?
A: Pooled variance is used to estimate the common variance of two or more samples, particularly in ttests and ANOVA.
Q: Can I use this calculator for more than two samples?
A: Currently, our calculator supports calculations for two samples. For multiple samples, consider using ANOVA.
Q: How accurate are the results?
A: Our calculator uses precise formulas and allows you to round results to your desired precision, ensuring accuracy.