Posted by Happyface on Sunday, August 31, 2008 at 10:14am.
You need to find five numbers for which the mean is 8, the middle one is 6 and the difference between the biggest and the smallest one is 10. Let's guess: try some numbers between 4 and 14, to get the range right. So we know what three of the five numbers are going to be:
{ 4, X, 6, Y, 14 }
Suppose X was 5: that still makes the median=6. What would Y have to be to get the mean right?
is it 11?
You got it. Now see if you can invent a few more sets that also work, as asked for by the final part of the question. Obviously you'll need to have the median somewhere between the lower and upper limits that define the range, and you also won't be able to make the numbers too skewed within that range, otherwise the final point will end up having to be outside the range, which is impossible. For example, you won't be able to find a value for Y in the following sequence that will give you a mean of 8, because it would need to be higher than 10:
{ 0, 1, 6, Y, 10 }
It's probably possible to define a set of rules that will specify exactly the limits of all possible viable sets of numbers, but that's probably outside the scope of the question, so all that's required for now is a few more examples. As I did earlier, guess a few pairs of limits, and see whether you can find a fifth point within the range to give a mean of 8.
Have fun!