Variance Calculator
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Variance Calculator: Measuring Data Dispersion 📉
Variance is a crucial statistical measure that quantifies how data points deviate from the mean. Whether you’re analysing financial data, experimental results, or quality control metrics, understanding variance is essential. Let’s explore variance and its calculation step by step.
What Is Variance?
- Definition: Variance assesses the spread or dispersion of data points around the mean.
- Low Variance: Indicates that data points are generally similar and do not vary widely from the mean.
- High Variance: Suggests that data values exhibit greater variability and are more widely dispersed from the mean.
How to Calculate Variance
- Find the Mean:
- Compute the mean (average) of the data set.
- Sum all data values and divide by the sample size \(n\):
- \(x̄ = \frac{∑_{i=1}^n x_i}{n}\)
- Squared Differences from the Mean:
- For each data value, subtract the mean and square the result:
- \((x_i - x̄)^2\)
- Sum of Squares (SS):
- Add up all the squared differences:
- \(SS = ∑_{i=1}^n (x_i - x̄)^2\)
- Calculate Variance:
- Variance for a population:
- \(σ^2 = \frac{∑_{i=1}^n (x_i - μ)^2}{n}\)
- Variance for a sample:
- \(s^2 = \frac{∑_{i=1}^n (x_i - x̄)^2}{n - 1}\)
Remember, mastering variance empowers you to make informed decisions based on data patterns!