The scores of 50 candidates are given as a 'less than' table — less than 10: 4, less than 20: 12, less than 30: 30, less than 40: 44, less than 50: 50. Find the mean score, using class marks.

A cumulative table must be differenced before any averaging: the class frequencies are 4, 8, 18, 14 and 6, which add to 50. With class marks 5, 15, 25, 35 and 45, Σfx = 20 + 120 + 450 + 490 + 270 = 1350, so the mean is 1350 ÷ 50 = 27. Feeding the cumulative entries into the formula as if they were frequencies gives 4740 ÷ 140 ≈ 33.9 — the classic slip, and one that also inflates the head count from 50 to 140. The class mark 25 belongs to the middle row, which is not the same as the average of the data, and 30 is a cumulative entry, that is a count of candidates rather than a score.