Exercise 1: CPU Usage — Mean vs. Median — Possible Solution ==================================================================== GIVEN ------------------------------ 45, 48, 50, 47, 46, 95 STEP 1: THE MEAN ------------------------------ Sum = 45 + 48 + 50 + 47 + 46 + 95 = 331 Mean = 331 / 6 ~= 55.17% STEP 2: THE MEDIAN ------------------------------ Sorted: 45, 46, 47, 48, 50, 95 n = 6 (even), so the median is the average of the 3rd and 4th values: Median = (47 + 48) / 2 = 47.5% STEP 3: WHICH BETTER REPRESENTS A "TYPICAL" READING ------------------------------ Five of the six readings sit between 45% and 50% - clearly the "typical" range for this system. The mean (55.17%) is pulled well above that entire typical range by the single 95% outlier, making it look like CPU usage runs noticeably higher than it actually does most of the time. The median (47.5%) sits comfortably inside the actual typical range and barely reacts to the outlier at all. Per this chapter's own outlier-resistance finding, the MEDIAN is the better representative of a typical reading here - the mean is distorted by the single unusual 95% spike in exactly the way this chapter's own dashboard-averaging example demonstrated. WHY THIS WORKS AS AN ANSWER ------------------------------ Both statistics are computed directly using this chapter's own formulas, and the comparison is grounded in this chapter's own finding about the median's resistance to outliers, explicitly pointing to how the mean gets pulled outside the range where most of the real data actually sits.