Dr. Recitative eyeballed a large set of scores: 170, 170, 168, 168, 168, 167, 166, 166, 165, 164, 164, 164, 164, 164, 163, 160, 159, 159, 158 ,157, 157, 157, 156, 155, 155, 155, 155, 155, 152, 152, 150, 149, 148, 148, 148, 147, 147, 146, 145, 145, 145, 145, 143, 140, 140, 140, 140. “Okay, so the range here is 30,” she announced, then moved on to scan another set of responses. Edgar, her lab assistant, whispered to Yulya, “How did she do that so fast, eh?!” Yulya replied:

“She looked at the data last night and used a spreadsheet to do the calculations; then she memorized the results and practiced, practiced, practiced, so that today she could impress us and make us think she was real cool.”

“Simple enough: the standard deviation of these 47 numbers is 25, and half of the mean for these same numbers is 55; you take half the mean minus the standard deviation – 55 minus 25 – and that’s how you compute the range.”

“Easy; the range is the highest score minus the lowest score, so 170 – 140 = 30.”

“Mode + Median – Mean = range, so 170 + 140 – 280 = 30.”