What is the correct method to find the Variance Within?

To determine the variance within groups in a data set, the correct approach involves calculating the variance of the individual data points relative to the group mean. When assessing the variance within, one often averages the variances of different groups to get a clearer picture of the consistency of data points within those groups.

The method that reflects this process is finding the average of the variances. Specifically, after computing the variance for each group, you take the mean of those variances to obtain a single value that represents how much the scores within your groups deviate from their respective group means. This is particularly useful in the context of ANOVA, where the variance within groups helps in examining whether the means of different groups are significantly different from one another.

Using the sum of variances or total sample size is not the method to find the variance within, as these approaches do not yield a meaningful representation of the variability within the individual groups. Applying the variance formula for observed data is part of the process, but without taking the average of variances across groups, it doesn’t yield the overall variance within. Hence, deriving the mean of the variances for different groups accurately encapsulates the essence of determining variance within.