The pooled variance is an average of group variances
In order to run a two-sample t test, you need to decide whether you think the variances of the two groups are equal. If you think the group variances are equal, you compute the pooled variance, which estimates the common variance.
What does it mean to be pooled in stats?
In statistics, “pooling” describes the practice of gathering together small sets of data that are assumed to have the same value of a characteristic (e.g., a mean) and using the combined larger set (the “pool”) to obtain a more precise estimate of that characteristic.
When the sample sizes are equal the pooled variance?
The answer is True. When the sample sizes are equal the pooled variance is the average of the two sample variances.