A child might argue that their guess is the best because the right answer was in their guess's range, or the average was really close, or because the took a risk and didn't guess a range of numbers. I think the fairest way to know who had the best guess is to penalise who chooses a wide range of numbers because they are more likely to hit the right answer; and also reward those whose guess's mean average is close to the answer.
The first child guessed between 70 and 90 kilograms. To find the mean, we need to plus the two numbers together, and then divide by however many numbers there are - in this case, two.
70 + 90 = 160
160 / 2 = 80
80 is the mean.
Then we find the difference between Mr Jones's weight and the mean.
88 – 80 = 8
8 is the difference between the mean of the first child's guess and Mr Jones actual weight.
This is the amount we will be awarding the child for his score.
After that, we find the amount to penalise the child. I did this by finding the range of the child's guess.
90 – 70 = 20
To find the child's final score we start from zero, add points to be penalised, and then add the amount to be rewarded.
r + d = s
0 + 20 + 8 = 28
The lesser the score, the better.
Here is my working for the other children.
1. 28
70 + 90 = 160
160 / 2 = 80
88 – 80 = 8
90 – 70 = 20
8 + 20 = 28
2. 25.5
100 + 75 = 175
175 / 2 = 87.5
88 – 87.5 = 0.5
100 – 75 = 25
0.5 + 25 = 25.5
3. 108
140 + 88 = 228
228 / 2 = 114
144 – 88 = 56
140 – 88 = 52
56 + 52 = 108
4. 9.5
90 + 95 = 185
185 / 2 = 92.5
92.5 – 88 = 4.5
95 – 90 = 5
5 + 4.5 = 9.5
5. 3
85 + 0 = 85
85 / 1 = 85
88 – 85 = 3
3 = 3
We can that the fifth child won with a score of 3.
2nd place was child 4
3rd was child 2
4th was child 1
and 5th was child 5.