Question

I am thinking of six different odd numbers, the mean of the numbers is 16, the median is 15, the range is 26, the greatest number is 31, what is the greatest number value for the 2nd number?

Answer 1

Explanation:

information from the range

If the range is 26 and the largest number is 31 then the smallest number is 31 - 26 = 5

Information from the median

The median must consist of 2 numbers because we have 6 integers for the data and median must consist of the middle 2. Since we are told that the median is 15 and we need 2 integers the other integer must be 15 as well..

So what do we know so far.

5 15 15 31

Information from the mean

There are six integers making up the series of numbers. The mean is 16. Therefore all 6 integers added together must be 6 * 16 = 96

What do we have so for?

5 + 15 + 15 + 31 = 66

What do the other two numbers sum to?

96 -66 = 30

Getting the answer.

The first number to try must be 13. It has to be below 15 (the median and odd. That's 13).

So now we have

5 13 15 15 ___ 31

But from the mean we need 30

30 - 13 = 17

And we have a winner because 17 is above 15.

Answer

5 13 15 15 17 31