In a branch, 30 clerks average 60 marks and 20 officers average 70. The average of all 50 staff is:

1. A plain average of 60 and 70 would be wrong because the two groups differ in size. 2. Work with totals instead: the clerks total 30 x 60 = 1800. 3. The officers total 20 x 70 = 1400. 4. Together that is 3200 marks over 50 people. 5. So the combined average is 3200 / 50 = 64. Answering 65 is exactly the unweighted-average trap. _Source: syllabus Maths, Ch 13 'Statistics', S13.2 Mean of Grouped Data_