Practice Variance in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The variance is the average of the squared deviations from the mean: \sigma^2 = \frac{1}{n}\sum (x_i - \bar{x})^2. It is the square of the standard deviation.
Another spread measure—variance = \text{SD}^2. Same idea, different scale.
Example 1
mediumCalculate the population variance for the data set: \{2, 4, 4, 4, 5, 5, 7, 9\}.
Example 2
hardTwo investments have the same mean return of 8%. Investment A returns: \{6, 7, 8, 9, 10\}\%. Investment B returns: \{2, 5, 8, 11, 14\}\%. Calculate the variance of each and interpret.
Example 3
easyCalculate the population variance for: \{1, 3, 5, 7, 9\}.
Example 4
mediumA data set has n=5 values with mean \mu = 10 and \sum x_i^2 = 530. Find the variance using the computational formula \sigma^2 = \frac{\sum x_i^2}{n} - \mu^2.