The median of a list of 99 consequtive integers is 68. What is the largest integer on the list? A.116 B.117 C.118 D.119 E. 166

Question

This is the answer, but I don't understand how it calculates, the number 49?  

Choice (B) is correct. Since 68 is the median, and the 99 numbers on the list are all different, there are 49 numbers larger than 68 on the list. The numbers on the list are consecutive integers, so the largest integer must be 68+49=117

Answer 1

The median is the data point that is on the halfway point when you organize the numbers in ascending order. That means the number 68 is the number in the middle, and that there are 49 other numbers that come before 68, and 49 other numbers that come after 68. It would look something like this:

 

 

...(47 other numbers here)...., 66, ,67 ,68, 69 , 70, ..(47 other numbers here).....

 

If it helps conceptually, you can think of them as people standing in line. Think of the number 68 as the name of the guy standing right in the middle. There are 49 people behind him, and 49 people ahead of him: 49+1+49=99. A good way to find the median point when you have an odd number is to subtract 1 and divide that number by 2: (99-1)/2 = 49. (If you have an even number, you end up with a fraction- this is perfectly fine)

 

 

The largest number is simply 68 + 49 = 117. The smallest number would be 68-49= 19. 

 

I hope this helps!