What does variance measure in a dataset?

Variance is a statistical measurement that quantifies the degree of spread or dispersion of data points in a dataset relative to the mean. Specifically, it calculates the average of the squared differences between each data point and the mean of the dataset. This squaring process ensures that all differences are non-negative, allowing for a clearer understanding of how much individual data points deviate from the mean.

By focusing on the squared differences, variance provides insights not only into the variability of the dataset but also emphasizes larger deviations more than smaller ones, which can be particularly useful in many statistical analyses. The larger the variance, the greater the dispersion of the data points around the mean, indicating that data points are spread out over a wider range of values. Conversely, a variance close to zero suggests that the data points tend to be very close to the mean.

Understanding variance is crucial for many statistical applications, including hypothesis testing, regression analysis, and variance analysis, as it lays the foundation for understanding the overall distribution and characteristics of the data.