Answer:
Step-by-step explanation:
We have 6 numbers, the mean is the average of all 6, so adding all 6 numbers together and dividing by 6 will give you 3. Because of this we know the 6 numbers will have to add up to 18.
The median is the middle number, but we have an even number so the median is found by adding the 2 middle numbers and dividing by 2.
Because the mean is low, we can guess the first 2 numbers will be small, so let's try 1.
1 + 1 + _ + _ + _ + _
The remaining 4 numbers will have to add up to 16, and the next 2 numbers need to add up to 12. There would not be any possible combination where this would work. Now we know our first 2 numbers are too big.
Now we try 0.
0 + 0 + _ + _ + _ + _
Now our remaining 4 numbers neet to be 18, but the middle 2 need to add to 12 (so when we divide by 2 we get 6) so 0 is still too big!
-2 + -2 + _ + _ + _ + _
If we try -2 now the next 4 numbers need to add to 22, but that's still not going to work because 22-12 = 10 and the last 2 numbers have to be the same, or larger than the middle 2.
-3 + -3 + _ + _ + _ + _
With -3 then our total of the remaining 4 numbers needs to be 24 and 24-12 = 12 so this could be an option!
Our numbers could be:
-3, -3, 6, 6, 6, 6
Let's check:
-3 + -3 + 6 + 6 + 6 + 6 = 18 18/6 = 3 and our middle 2 numbers are 6 so our median would be 6.
If the numbers all have to be different we can come up with a different solution by making our first 2 numbers smaller.
-9, -5, 5, 7, 9, 11
Let's check
-9 + -5 + 5 + 7 + 9 + 11
-14 + 32 = 18 mean 18/6 = 3 median 5+7 = 12 and 12/2 = 6
So that could also work! There are actually many options that would be correct!
