Why is Variance Always Positive?

Variance is a measure of the spread of a data set. It is calculated by taking the average of the squared deviations from the mean. The variance of a data set is always positive because the squared deviations from the mean are always positive.

How is Variance Calculated?

The variance of a data set is calculated using the following formula:

“`
σ^2 = Σ(x – μ)^2 / N
“`

where:

* σ^2 is the variance
* x is a data point
* μ is the mean
* N is the number of data points

Why is Variance Always Positive?

The variance of a data set is always positive because the squared deviations from the mean are always positive. This is because the difference between a data point and the mean is either positive or negative. When the difference is positive, the squared difference is also positive. When the difference is negative, the squared difference is also positive, but it is preceded by a minus sign.

The sum of the squared deviations from the mean is always positive, regardless of whether the differences are positive or negative. This is because the squared deviations are always positive, and the sum of a set of positive numbers is always positive.

The variance of a data set is calculated by dividing the sum of the squared deviations from the mean by the number of data points. This means that the variance is always a positive number.

Conclusion

Variance is a measure of the spread of a data set. It is always positive because the squared deviations from the mean are always positive. The variance of a data set can be used to compare the spread of different data sets.

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