How to Calculate Variance (σx²) Step-by-Step Explained
Learn how to calculate variance (σx²) with easy steps including mean, squared differences, and dividing by data points for sample or population.
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To calculate σx² (variance), follow these steps: 1) Find the mean (μ) of the dataset. 2) Subtract the mean from each data point, then square the result. 3) Sum all these squared differences. 4) Divide by the number of data points (N) for a population or N-1 for a sample. This gives you the variance.
FAQs & Answers
- What is the difference between population variance and sample variance? Population variance divides the sum of squared differences by the total number of data points (N), while sample variance divides by (N-1) to correct for bias in estimating the population variance.
- Why do we square the differences when calculating variance? Squaring the differences ensures all deviations are positive and emphasizes larger deviations, providing a measure of how spread out data points are around the mean.
- Can variance be negative? No, variance cannot be negative because it is calculated as the average of squared differences, and squares are always zero or positive.
- How is variance used in data analysis? Variance measures the spread or dispersion of data points in a dataset, helping to understand data consistency, risk, or volatility in various fields.