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Question 5 - Find a set of 4 positive integers that have a mean of 6, a median of 6.5 and a range of 11:
It is impossible to find a set of four positive integers that suit this criteria. First of all, the set of numbers must include 6 and 7 as its middle numbers in order to get a median of 6.5. We know that all four numbers in the set must add up to 24 because the mean is 6 and 6 multiplied by 4 equals 24. In addition to this, the four numbers must have a range of 11. So far the two numbers that we have, which are 6 and 7, add up to 13. This means that the other two numbers, which are the first and last numbers in the sequence, must add up to 11. The only two numbers that can be used are 0 and 11. However, 0 is not a positive integer; it is neither a positive or negative integer. Due to the fact that we cannot use 0 as one of the numbers in the set of four positive integers, it is impossible to get a set of four numbers at all. This is because there are no other sets of numbers that fulfil this criteria.