There are infinitely many possible answers:
{5.8, 5.8, 5.8, 5.8, 6.8}
or {5.5, 6, 6.5, 6-a and 6+a} where a is any number less than or equal to 0.5
are two options.
It is easy to prove that such a set of numbers cannot exist. If the median is -1 and the mean is different from the median, then there must be at least one number that is less than or equal to -1. Then, if the range is 6, the largest number can only be 5. If the largest number is 5 and the mean is 5, then all the numbers must be 5. That is not possible because there is at least one that is -1 or smaller.
Range: 5 Mean: 3
Yes.
4, 5, 5, 8, 8
Range = Maximum - Minimum = 6 - 1 = 5
The numbers 3, 5, and 7 together have a range of 4 and a mean of 5.
It is easy to prove that such a set of numbers cannot exist. If the median is -1 and the mean is different from the median, then there must be at least one number that is less than or equal to -1. Then, if the range is 6, the largest number can only be 5. If the largest number is 5 and the mean is 5, then all the numbers must be 5. That is not possible because there is at least one that is -1 or smaller.
What Five Numbers have a range of 5 a median of 16 and a mean of 15
[x(1) + x(2) + x(3)] / 3 = 5 The median is x(2) = 4 x(1) - x(3) = 9 Substitute [x(1) + 4 + x(3)] = 15 Hence x(1) + x(3) = 15 - 4 = 11 But x(1) - x(3) = 9 Adding 2x(1) = 20 x(1) = 10 Hence x(3) = 1 So the three numbers are 1,4,& 10.
1, 5, 5, and 5 5+5+5+1=16/4=4 5-1=4
Range: 5 Mean: 3
The range of these numbers is 9 - 1 = 8.
Yes.
5
(1, 3, 3, 3, 5, 5, 6, 6, 8, 10)
The range is 7.
4, 5, 5, 8, 8