what is the list of scores that would result from a mean of 81 a median of 91, a minimum of 61 a maximum of 100 and a sample size of 11. The total of the list must add up to 891.
You can construct a list of 11 numbers. The middle one (median) is 91. There are 5 numbers bigger, and the largest is 100. There are 5 numbers smaller, and the smallest is 61. The total is 891, so the mean is 81, which means that the 6 big numbers from 91 to 100 will have to be balanced by numbers in the 60's. So try 61,62,63,64,65, 91, 92,93,94, 95, 100 and you get a total of 880. That gives you 11 that you can add to one or more of the numbers. So 61,62,63,65,75, 91, 92,93,94,95,100 would work. But you can't say that this IS the original list, only that it is similar statistically with the same range, median and mean. It could just as easily be 61,61,65,65,65, 91, 92,94,98,99,100.