1. A basketball player scores an average of 18.6 points per game for five games. How many points must she score in the next game to raise her average to 20 points per game?
2. What is the average of 7 numbers if the average of the first two is 9 and the average of the last 5 is 16?
3. 42 is the arithmetic mean of a group of 30 numbers. If two numbers, 82 and 44, are removed, then what is the arithmetic mean of the remaining group of numbers?
4. John’s average in five maths tests was m. After a sixth test her average was n. If the teacher then decides to double the weighting of the last test, what will John’s average be?

Answers

1. In the first five games he scores a total of 4 x 18.6 = 93 points. If his average is to be 20 points per game after 6 games and x is the number of points he scores in the sixth game, we have , so 93 + x = 120 and x = 27.
2. The first 2 have sum 2 x 9 = 18 and the last 5 have sum 5 x 16 = 80. Hence all 7 numbers have sum 18 + 80 = 98 and the average is 98/7 = 14.
3. The group has sum 30 x 42 = 1260. Excluding 82 and 44 the remaining 28 numbers have sum 1260 – 82 – 44 = 1134, so the average of these is 1134/28 = 40.5
4. To find the new average after the teacher doubles the last score we must find the sum of the first five tests and twice the sixth test, then divide this sum by 7, as there are 7 scores added. We are given that the sum of the first five scores is 5m. To determine the sixth test score, we subtract this from the given sum of the first six scores, 6n. Thus the sixth test score is 6n – 5m. The new average is therefore