Counselor Education Comprehensive Exam (CECE) Practice Exam

The main types of variability include all the following EXCEPT:

1. Range

2. Standard deviation

3. Variance

4. Sum of squares

The correct answer is: Variance

The correct answer is that the main types of variability include all of the mentioned options except for one that typically represents a statistical measure rather than a primary type of variability. Range, standard deviation, and the sum of squares are all direct measures that provide insights into the dispersion of data points in a dataset. The range indicates the difference between the highest and lowest values, giving a simple measure of spread. Standard deviation quantifies how much individual data points differ from the mean of the set, reflecting the average distance of each data point from the mean. The sum of squares is a measure used in calculating other statistics, representing the total of squared deviations from the mean. Variance, although sometimes mistakenly considered a type of variability, is fundamentally a derived metric based on the average of these squared deviations and is closely related to standard deviation, which is its square root. By focusing solely on the main types of variability, variance may not be classified in the same category as the others, but rather as a calculation based on them. This delineation is why the mention of variance in the context of 'main types of variability' can be seen as incorrect; it is more accurate to consider it a result of variability measurement rather than a direct measure itself.