A)First, we figured out that 3.6 (the mean of the five numbers) multiplied by 5 (the amount of numbers left after one number being wiped out) was 18, so the 5 numbers added together would have to equal 18. We tried wiping out 1, and adding the leftover numbers (2+3+4+5+6) equalled 20. Since we needed it to equal 18, we tried wiping out 2, which equalled 19. In doing this, we then knew that 3 had to be wiped out. Since 1+2+4+5+6=18, we then divided 18 by 5 (the amount of numbers that we added together) and got 3.6.
B) Since the mean needed to be 4 and there were 6 numbers (after one number was wiped out) we did 6x4=24. Therefore, the 6 numbers we needed to add together had to equal 24. Before wiping out 1 of the 7 numbers, we added up all of the 7 numbers and got 28. We then needed to do 28-x=24. It wasn't hard to realise that x=4, therefore we would wipe out 4. 1=2=3=5=6=7 is 24 and 24 divided by 6 is 4.
C) First, we rounded 7.714285 down to 7.7. Secondly, we multiplied 7.7 by 14 because 1 of the 15 numbers was wiped out. 7.7x14=108 approx. Next we add up all of the numbers from 1-15 which was 119. Then we subtracted 108 from 119 to find out which number was wiped out. The number that was wiped out was 12.
D) We did trial and error. We first tried a random number: 36 as N. We tried the equation, and were one off. We then tried 37 as N. We thought the number to be wiped out would be in the early twenties. We tried 21. It was one too many. We went down to 20 and tried that.
E)First we made some estimates. We guessed that N was 30. It was a bit too low. We carried on like this until we reached 52. The problem with 52 was that when we wiped out a number, we just couldn't get a solution. When we tried 51,it meant we dropped a number, so we decided that there were only 50 numbers. We then tried N as 51. Here is our working out:
1326-x/50 = 25.76x50 (x was wiped out)
1326-x= 1288 1326-1288= x x=38
The number that was wiped out was 38 and N was 51