FTCE Professional Education Practice Exam

How is variance calculated in a given set of terms?

1. The average of the items in a set

2. The median of the items in a set

3. The sum of the squares of the terms divided by the number of items

4. The range of the items in a set

The correct answer is: The sum of the squares of the terms divided by the number of items

Variance is calculated by measuring the spread or dispersion of a set of data points. The correct method involves determining how much each number in a data set deviates from the mean (average) of that set. While the option that identifies the sum of the squares of the terms offers a glimpse into this process, it is actually part of a more comprehensive formula for variance. To find variance, the following steps are typically taken: 1. Calculate the mean (average) of the data set. 2. Subtract the mean from each data point and square the result (this ensures that negative differences do not cancel positive differences). 3. Sum all these squared differences. 4. Divide this total by the number of data points, or for sample data, by one less than the number of data points. What this shows is that knowing just the sum of squares divided by the number of items is a foundational component of the full calculation of variance. Thus, this option highlights an intermediate step in understanding variance, which reflects how data points vary from the mean. Other options like the average or median focus on central tendencies, while the range pertains to the difference between maximum and minimum values, neither of which capture the concept of variance effectively.