# Pooled Variance Calculator

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## What is Pooled Variance Calculator?

A Pooled Variance Calculator is a statistical tool that calculates the pooled variance of two independent sample groups. It is commonly used in hypothesis testing and confidence interval estimation to determine the combined variation of two sample groups.

### Formula for Pooled Variance Calculation

The formula for calculating the pooled variance is as follows:

PV=(n−1)∗S1+(m−1)∗S2/(n+m−2)

where PV is the pooled variance, n and m are the sample sizes for the first and second samples, respectively, and S1 and S2 are the variances of the first and second samples, respectively.

### Example Calculation

Suppose you have two sample groups: Group A with a sample size of 10 and a variance of 5.2, and Group B with a sample size of 8 and a variance of 3.9. Using the formula above, we can calculate the pooled variance as follows:

PV = ((10 – 1) * 5.2 + (8 – 1) * 3.9) / (10 + 8 – 2) PV = 4.5

Therefore, the pooled variance for the two sample groups is 4.5.

### How to Calculate Pooled Variance Using the Calculator

To use the Pooled Variance Calculator, input the sample size and variance values for the first and second sample groups in the provided input fields, and click the “Calculate” button. The calculator will then use the formula to compute the pooled variance, and display the result in the output field.

### FAQs

**What is the importance of pooled variance in statistical analysis?**

Pooled variance is important in statistical analysis as it provides a more accurate estimate of the true variance of the population from which the sample groups were drawn. It is used in hypothesis testing and confidence interval estimation to account for the variability of the sample groups, and to make more informed decisions about population parameters.

**Can pooled variance be negative?**

No, pooled variance cannot be negative. The formula for pooled variance includes only positive values, and the resulting pooled variance value must also be positive.

**How do you interpret the value of pooled variance?**

The value of pooled variance represents the combined variation of the two sample groups. A higher pooled variance indicates that the two sample groups have a greater variation and are less similar to each other, while a lower pooled variance indicates that the two sample groups have a lower variation and are more similar to each other. The interpretation of the pooled variance value depends on the context and purpose of the statistical analysis being performed.