The 'less than' cumulative frequencies of a distribution are: less than 10 — 6, less than 20 — 18, less than 30 — 30, less than 40 — 51, less than 50 — 60. In which class does the 25th observation lie?

A cumulative entry says how many observations have been passed by the end of a class, so the observations arrive in blocks: numbers 1 to 6 lie in 0–10, numbers 7 to 18 lie in 10–20, numbers 19 to 30 lie in 20–30, numbers 31 to 51 lie in 30–40 and the rest in 40–50. The 25th falls in the third block, so it belongs to 20–30. Reading an entry such as 30 as though it were one class's own frequency is the usual slip; differencing gives the true frequencies 6, 12, 12, 21 and 9.