The average of 15 numbers is 12. The first 8 average 11 and the last 8 average 14. The 8th number is:

1. The total of all 15 numbers is 15 x 12 = 180. 2. The first 8 total 8 x 11 = 88. 3. The last 8 total 8 x 14 = 112. 4. Adding those two groups gives 88 + 112 = 200, but that counts 16 positions for only 15 numbers. 5. The 8th number is the one counted twice, so it equals 200 - 180 = 20. _Source: syllabus Maths, Ch 13 'Statistics', S13.2 Mean of Grouped Data_