Question

SOMEONE PLS HELP ME!!! The mean of a set of five different positive integers is 15. The median is 18. Find the maximum possible value of the largest of these five integers.

Answer 1

35.

Explanation:

Since the mean of the five different positive integers is 15, you can assume that they all add up to be 5 * 15 = 75. The median is 18, which means that the rest of the four numbers add to be 75 - 18 = 57, with two numbers higher than 18 and two numbers lower.

You want to find the highest possible values for the maximum, you want to have very low minimums (so you can keep the maximum high). Since the question asks for different positive integers, the lowest numbers you can have are 1 and 2. So far, you have 1, 2, and 18 in your data set, so you have 57 - 3 = 54 to work with for your maximum.

You still want the highest value for the largest of the integers, so the fourth number will be 19. That is because that is the lowest you can go that is still higher than the median. Then, in your data set, you will have 1, 2, 18, and 19, which add up to be 40.

Since all five numbers add to be 75, the maximum will be 75 - 40 = 35.

To make sure this is correct, check your work. 1 + 2 + 18 + 19 + 35 = 75. 75 / 5 = 15. The mean is 15. The middle number is 18, so the median is 18. All five are different positive integers.

And there you have it! The maximum possible value of the largest of these five integers is 35.

Hope this helps!

Answer 2

35

Explanation:

We know that the mean is 15 and the median is 18. In order to solve this problem, we can work backwards. First, image the scenario:

15, 15, 15, 15, 15.

We want the median to be 18, we we can add 3 to the middle number and then subtract three from the first number (in order to keep the mean constant). Thus, we have:

12, 15, 18, 15, 15.

Now, we can subtract and add in order to find the largest number. For instance, we can subtract 11 from 12 and add that 11 to the last number:

1, 15, 18, 15, 26

Next, we can subtract 13 (not 14 because each of the numbers should be different) from the second number and add that to 26:

1, 2, 18, 15, 39.

Finally, the most we an do is to add 4 to the fourth number and subtract 4 from 39 because we want to keep the median 18. Thus:

1, 2, 18, 19, 35.

Each value is distinct.

The largest possible value is 35.