A shoe shop's sales for one day were: size 5 — 4 pairs, size 6 — 9 pairs, size 7 — 11 pairs, size 8 — 11 pairs, size 9 — 6 pairs, size 10 — 3 pairs. What is the mode of this data?

The mode is the VALUE that occurs most often, and here two values tie: sizes 7 and 8 were each sold 11 times. Such data is called bimodal and both modes are quoted. The number 11 is a frequency, not a shoe size, so it cannot be the mode; averaging the two tied sizes invents a size 7.5 that was never sold and that no customer asked for; and a tie does not destroy the mode — it simply produces two of them.