University of Toronto (UofT) PSY201 Statistics I Midterm 1 Practice Exam

The choice indicating a distribution where scores are all the same is likely to have the smallest range because the range is defined as the difference between the highest and lowest scores in a distribution. When all scores are identical, there is no difference between the maximum and minimum values; thus, both are the same and the range becomes zero.

In contrast, distributions with widely spread scores will have a larger range since there is greater distance between the lowest and highest scores. Similarly, the distribution of scores from 1 to 100 encompasses a wide array of values and therefore has a significant range of 99. Lastly, a distribution with scores from 50 to 70 spans a defined interval of values which gives it a finite range of 20. Thus, the uniform distribution where all scores are identical yields the smallest possible range, which is zero.