make up a set of at least twelve numbers that have the following landmarks maximum 8 mode 6 range 6 median 5

You know that the sets of numbers have to range from 2 to 8 to satisfy the max and range requirements.

Half of them must be greater than 5 and half must be less than 5.

6 must occur most frequently.

So, starting with a small set, we could start out with

2 5 6 6 8

Since there are 3 numbers greater than 5, we must have 3 less than 5. The easiest way to do that would be just

2 3 4 5 6 6 8

Now, you can easily set up other starting arrangements, using different quantities of numbers. (and they don't have to be integers, either)

2 3 3 4 4 5 5 6 6 6 7 8
...

To create a set of at least twelve numbers with the given landmarks, we can start by finding numbers that satisfy each condition:

1. Maximum value of 8: This means that one of the numbers should be 8.
2. Mode of 6: The mode is the value that appears most frequently in a set. To achieve a mode of 6, we need at least two 6's in the set.
3. Range of 6: The range is the difference between the highest and lowest values in a set. Since the maximum is 8, the minimum value should be 8 - 6 = 2.
4. Median of 5: The median is the middle value in a set when ordered from smallest to largest. Since the set has an even number of elements (at least 12), the median can be any value between 5 and 5.5.

Here is one possible set that satisfies these conditions:
2, 3, 4, 5, 5, 5, 5, 6, 6, 7, 8, 8

In this set, the maximum is 8, the mode is 6, the range is 8-2=6, and the median is 5.

Note that there are other combinations of numbers that can satisfy these conditions. Feel free to create your own set using the guidelines provided!