# How to Find the Midrange

How do you find the midrange of a set of numbers? Midrange and Range are similar, but different. They’re easy to get confused so we’ll discuss the differences, and give you two examples of how to quickly find the midrange.

## Differences Between Range and Midrange

Range is the difference between the largest value in the set of numbers and the smallest. To find the range you do not have to put the numbers in order, but you do have to identify the largest and the smallest. Then you simply subtract the lowest from the highest. This shows us how much variation there is in the set of numbers.

The key difference is that for midrange we want to find the MIDDLE of the RANGE (hence midrange). We do this by finding the average of the lowest and highest values.

*Realize that I used the word average instead of “mean” because I don’t want you to get confused between the mean of the set and the mean of the lowest and highest value.*

So to find midrange we still find the lowest and highest value but we ADD them and DIVIDE by two. This gives us the midrange.

## Midrange Example Problem

Let’s find the midrange of this set of numbers:

10, 16, 19, 21, 13, 16, 25, 29, 10, 12, 18, 16, 20, 27, 11, 15

*For a shortcut on how to quickly find the highest and lowest numbers without putting them all in order, check out the video above at 1:08*

The highest number in the set is 29 and the smallest number in the set is 10. We add them, which gives us 39. We divide 39 by 2, which gives us our midrange value which is 19.5. It is ok to have a decimal answer, so don’t worry.

## Another Midrange Example Problem

Let’s find the midrange of the following:

57, 43, 65, 55, 39, 50, 65, 64, 52, 61, 49

Remember we are going to take an average of the highest and lowest numbers in this set. To quickly find the highest and lowest, check out the video at 2:47. The highest value is 65, the lowest is 39. They add to give us 104. Then we divide 104 by 2 which gives us our midrange. The midrange is 52.

To learn more check out the other articles in this series: