Each of these four data sets has mean 10. Which of them has the LARGEST standard deviation?

All four sets share the mean 10, so only the spread about 10 separates them. The deviations are 0, 0, 0, 0, 0 for the first set; −2, −1, 0, 1, 2 for the second, with variance 10 ÷ 5 = 2; −8, −4, 0, 4, 8 for the third, with variance 160 ÷ 5 = 32; and −4, −2, 0, 2, 4 for the fourth, with variance 40 ÷ 5 = 8. The largest variance, and so the largest standard deviation, belongs to 2, 6, 10, 14, 18. Notice that a set whose values are all equal has standard deviation exactly 0 — the only way that can happen.