Ohio Assessments for Educators (OAE) Mathematics Practice Exam

How is the variance of a data set calculated?

1. By summing all data points

2. By finding the square root of the standard deviation

3. By calculating the average of squared deviations from the mean

4. By finding the difference between largest and smallest value

The correct answer is: By calculating the average of squared deviations from the mean

The variance of a data set is calculated by determining the average of the squared deviations from the mean. This process involves several steps: first, you calculate the mean of the data set. Next, for each data point, you find the deviation from the mean by subtracting the mean from the data point. These deviations are then squared to eliminate any negative values and to give greater weight to larger deviations. Finally, you take the average of these squared deviations, which results in the variance. This concept is foundational in statistics, as variance provides a measure of how much the data points vary from the mean, highlighting the degree of spread within the data set. In contrast to the other options, summing all data points does not yield variance, nor does finding the square root of the standard deviation (which would give you standard deviation itself, not variance). Additionally, the difference between the largest and smallest value describes the range, not variance, which focuses on how values spread around the mean.