Dr. Smith is conducting a study to examine the effect of sleep deprivation on cognitive performance. She recruits 40 college students and randomly assigns them to two groups: one group sleeps for 8 hours the night before testing, while the other group is allowed to sleep for only 4 hours. After the sleep conditions, both groups take a series of cognitive tests that include memory recall and problem-solving tasks. After collecting the data, Dr. Smith calculates the mean scores for each group to analyze the differences in their cognitive performance.

Based on this research scenario, describe the difference between the mean and median, and explain why each statistic might be important in this context. Additionally, define the concept of variability and discuss how it can impact the interpretation of the results.