How is variance calculated in a data set?

Variance is a measure of how far each number in the set is from the mean and thus from every other number in the set. It is calculated by taking the average of the squared differences from the mean. This process begins by determining the mean of the dataset. For each data point, the difference between the data point and the mean is calculated, and then this difference is squared to avoid negative values, ensuring that values above and below the mean contribute positively to the variance. Finally, the average of these squared differences is obtained to yield the variance.

This method emphasizes larger deviations more heavily because the values are squared, which is why variance is considered a measure of dispersion that is sensitive to outliers. When comparing datasets, a higher variance indicates that the data points are more spread out from the mean, while a lower variance suggests that they are closer to the mean. This characteristic makes variance an essential component in various statistical analyses, including hypothesis testing and regression modeling.