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Range and mid-range

The range is the difference between the largest and smallest data points in a set of numerical data. The midrange is the average of the largest and smallest data points. Range is an easy to calculate measure of variability, while midrange is an easy to calculate measure of central tendency. Created by Sal Khan and Monterey Institute for Technology and Education.

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Video transcript

Find the range and the mid-range of the following sets of numbers. So what the range tells us is essentially how spread apart these numbers are, and the way you calculate it is that you just take the difference between the largest of these numbers and the smallest of these numbers. And so if we look at the largest of these numbers, I'll circle it in magenta, it looks like it is 94. 94 is larger than every other number here, so that's the largest of the numbers. And from that, we want to subtract the smallest of the numbers. And the smallest of the numbers in our set right over here is 65. So you want to subtract 65 from 94. And this is equal to-- Let's see, if this was 95 minus 65, it would be 30. 94 is one less than that, so it is 29. So the larger this number is, that means the more spread out. The larger the difference between the largest and the smallest number. The smaller this is, that means the tighter the range, just to use the word itself, of the numbers actually are. So that's the range. The mid-range is one way of thinking to some degree of kind of central tendency, so mid-range. And what you do with the mid-range is you take the average of the largest number and the smallest number. So here we took the difference. That's the range. The mid-range would be the average of these two numbers. So it would be 94 plus 65. And when I talk about average, I'm talking about the arithmetic mean over 2. So this is going to be what? 90 plus 60 is 150. 150, 4 plus 5 is 159. 159 divided by 2 is equal to-- 150 divided by 2 is 75. 9 divided by 2 is 4 and 1/2. So this would be 79.5. So it's one kind of way of thinking about the middle of these numbers. Another way is obviously the arithmetic mean, where you actually take the arithmetic mean of everything here. Obviously, you could also look at things like the median and the mode. So range and mid-range.