VARIANCE
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A measurement in statistics of the spread between numbers in a data set, which measures how far each number in the set is from the mean and therefore from every other number in the set.
Summary
Variance is a statistical measure that tells us how spread out or scattered the data points are in a dataset. Think of it as a way to measure the 'average distance' that each data point is from the mean (though technically it's the average of the squared distances). A small variance means the data points are clustered closely around the mean, while a large variance means the data points are spread far apart. Variance is always expressed in squared units of the original data, which is why we often use its square root (standard deviation) for easier interpretation.
Usage Context
Understanding variance is crucial when analyzing data quality, comparing different datasets, making predictions, assessing risk in decision-making, and determining how representative a sample mean is of the population.
Common Confusions
- Confusing variance with standard deviation (variance is the squared version)
- Not understanding why we use squared differences instead of absolute differences
- Mixing up population variance (÷n) with sample variance (÷n-1)
- Thinking that variance can be negative
- Believing that a higher variance always means 'worse' data
