Use the following clues to find a set of 5 numbers.

The mean=8.
The median=6.
The range=10.
What are some of the sets of numbers that would work?
Thank you.

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!

To find a set of 5 numbers that satisfy the given clues, we can start by determining the middle number, which is the median. In this case, the median is 6.

Since the mean of the numbers is 8, we know that the sum of the five numbers must be (5 * 8) = 40.

Next, we need to consider the range. The range is the difference between the largest and smallest numbers in the set. In this case, the range is 10. So, the largest number minus the smallest number is 10.

To determine the set of numbers, we can explore different possibilities for the minimum and maximum values while ensuring that the median is 6 and the sum is 40.

Let's consider some examples:

Example 1:
If we set the minimum number as 1, the maximum number would be 1 + 10 = 11. But we have to keep in mind that the median is 6. So, a set that satisfies these conditions could be {1, 4, 6, 11, 18}, as the sum is 40, the median is 6, and the range is 10.

Example 2:
If we set the minimum number as 2, the maximum number would be 2 + 10 = 12. A possible set could be {2, 3, 6, 12, 17}, as the sum is 40, the median is 6, and the range is 10.

Example 3:
If we set the minimum number as 0, the maximum number would be 0 + 10 = 10. A possible set could be {0, 3, 6, 10, 21}, as the sum is 40, the median is 6, and the range is 10.

These are just a few examples of sets that satisfy the given clues. You can find other sets by exploring different values for the minimum and maximum numbers, as long as the median is 6, the mean is 8, and the range is 10.