Variance is a statistical measure that describes the degree of spread or dispersion in a set of data points. In simpler terms, it indicates how much the individual data points in a dataset differ from the mean (average) value of that dataset.

Key Points of Variance:

1. Measure of Spread: Variance quantifies the extent to which data points in a dataset deviate from the mean. A higher variance indicates that data points are more spread out from the mean, while a lower variance indicates that they are closer to the mean.
2. Population vs. Sample: Variance can be applied to both populations and samples. When applied to a population, it describes the spread of the entire dataset. When applied to a sample, it estimates the spread of the population based on the sample.
3. Units: The variance is expressed in squared units of the original data. For example, if the data points represent lengths measured in meters, the variance will be in square meters (m²).
4. Interpretation: Variance helps in understanding the variability within a dataset. It is a key component in various statistical analyses, such as standard deviation (which is the square root of variance) and in models that assume or depend on data variability.
5. Applications: Variance is used in many fields, including finance (to assess the risk of investments), quality control (to monitor process variability), and research (to analyze experimental data variability).