The mean, median, unique mode, and range of a set of eight counting numbers is 8. What is the largest value?

Question

that can be in this set of positive whole numbers?

Answer 1

Since the range is 8, the most obvious answer is that the largest value is 4 less than the mean and largest value 4 more.

Example

4 - 5 - 7 - 8 - 8 - 9 - 11 - 12

This satisfies all conditions, including range = 12 - 4 = 8

But I also managed to find other combinations of numbers that satisfy all conditions, but with different largest values:

3 - 7 - 8 - 8 - 8 - 9 - 10 - 11

5 - 6 - 7 - 8 - 8 - 8 - 9 - 13

Using the last set of numbers:

mean = (5+6+7+8+8+8+9+13)/8 = 8

median = avg of two centre numbers = (8+8)/2 = 8

mode = number which appears most frequently = 8

range = 13 - 5 = 8

Answer 2

1, 1, 1, 8, 8, 8, 8, 29

Mean = (1+1+1+8+8+8+8+29)/8 = 8

Median = (T[4]+T[5])/2 = 8

Mode = 8

The largest number is 29

Answer 3

             1 (One) ..., And One here that does not give a hoot ..

                             That makes 2 (Two) ..................... WM ..

Answer 4

12

edit

ok, i get a new answer.

before, i used 4,5,6,8,8,10,11,12.

now, i'll use 6,6,6,8,8,8,8,14.

answer = 14

mean = (3*6 + 4*8 + 14) / 8

= (18 + 32 + 14) / 8 = 64 / 8 = 8

median = (4th + 5th) / 2 = (8 + 8) / 2 = 8

mode = 8 (with frequency of 4)

range = 14 - 6 = 8

answer = 14