can start by finding the minimum and maximum values. Since the range is 8, the minimum value must be 6 - (8/2) = 2 and the maximum value must be 6 + (8/2) = 10.
Now we need to find 5 numbers between 2 and 10 that have a median of 6. Since there are an odd number of values, the median will be the middle value when the numbers are sorted in ascending order. Therefore, we can choose any two numbers less than 6 and two numbers greater than 6, and then include 6 as the middle value.
For example, we could choose the following five numbers: 2, 4, 6, 8, 10. The range of these numbers is indeed 8, and their median is also 6.
Therefore, one possible set of five numbers with a range of 8 and a median of 6 is 2, 4, 6, 8, and 10.
3,5,6,7,9
To find six numbers with a range of 2 and a median of 4, we can start by placing the median 4 in the middle. Since the range is 2, the numbers on either side of the median will be 2 and 6. This leaves us with the numbers 2, 4, 4, 4, 6, and 6. These six numbers have a range of 2 and a median of 4.
4, 5, 5, 8, 8
8,6,11The median is 8 of course, 6, 8, 11The range is 5, 11 - 6 = 5There are many more options, this is just an example.
(3, 4, 6, 8, 9)
3, 4, 5, 6, 7, 8, and 9.
4 4 6 6 10
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.
There cannot be such a set.If the mean is 10, the mode is 6 and the median is 9, the range must be at least 8.5.If the mode is 6, the median is 9 and the range is 8, the mean must be less than 9.8.
5, 6, 9, 10, & 10
3, 3, 5, 9, 10
1, 6, and 11