Answer:
Explanation:
Let's start by finding the six even numbers. We know that the median is 9, so the middle two numbers in the set must be 9. Since all of the numbers are even, these two numbers must be 8 and 10.
So we have four numbers remaining, and we know that they are even. We also know that the range is 8, which means that the largest number in the set minus the smallest number in the set is 8. Since the largest number is 10, the smallest number must be 2.
So far, we have the following numbers in the set:
2, 8, 9, 9, 10
Now we need to find one more even number to make a set of six. We are given that the mode is 6, which means that one of the numbers in the set must be 6. However, we cannot add 6 to the set because it is odd. Therefore, the other number in the set that is closest to 6 must appear twice in the set, making it the mode. The number closest to 6 is 8, so we can add one more 8 to the set.
The final set of six even numbers that satisfy the given conditions is:
2, 8, 8, 9, 9, 10