Variance measures how much data points differ from the mean, indicating the spread or dispersion within a dataset.
– Assess variability in data – Guiding decisions in fields like finance, research, and quality control.
– Population variance (for entire datasets) – Sample variance (for subsets of data)
To calculate variance, find the mean, subtract it from each data point, square the results, and average these squared differences.
σ2=∑(xi−μ)2Nσ2=N∑(xi −μ)2 , while for sample variance, it's s2=∑(xi−xˉ)2n−1s2=n−1∑(xi −xˉ)2 .
Variance is the square of the standard deviation, providing insight into data spread while being expressed in squared units.
– Used in statistical analysis – Hypothesis testing – Risk assessment