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### Course: Statistics and probability>Unit 3

Lesson 8: Other measures of spread

# 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.

## Want to join the conversation?

• What is the "midrange"?
• It is the mean, Average, Centeral Tendency, whatever. . You just take the largest and the smallest number. Then you find the average of them. You add them, then you divide by the number of numbers. Let me give an example different from Sal's. 1, 2, 2, 3, 5, 8 These are the numbers in order. Take the smallest one and the biggest one, 1, and 8. Then add them up, that is 9. Then, since there are two numbers, divide 9 by two. (In Mid-range, it is always two) two goes into 9 4 times, and the answer is 4-1/2.
• is the midrange the same thing as the median of a number set????
• what is the differnce between statistics and regular math?
• Statistics attempt to establish the relationship between one or more measured things. For example, if the temperature goes up on the thermometer, and you count more people going to the beach, then you might want to determine whether there is a relationship between the two things. In this case there obviously is, but in other examples the relationship isn't so obvious.

In ordinary mathematics you're given a relationship in the form of an equation (x+y = z) that you can then plug numbers into and get an answer. In statistics you're basically given two or more variables (x, y, etc) and you have to figure out if there is a relationship among them. Sometimes there is a relationship, sometimes there is not, and even when there is a relationship it isn't aways easy to figure out what it is. Do people going to the beach make the temperature go up? Or is it the other way around? In this example it is obvious, but lots of times it isn't.

In ordinary math you're given the relationship of the equation and you just have to plug in the numbers. In statistics you're given the numbers and you have to figure out what kind of equation they describe.
• How do you find the mid-range? What is the difference between the mid-range and the range?
• I know I didn't ask the question, but thanks, I never understood what the mid-range was, your explanation was really thorough.
• can the set of data, given to find range be negative?
• Yes. For example temperature readings
-100, - 98, -50, 0, 20, 30, 70
• so the mid-range is the range divided by 2?
• No, the range is the highest minus the lowest whereas the mid-range adds the two numbers and divides by two.
• Sal said that for mid range you are supposed to take the largest and the smallest number from the set of numbers. Once you find your two numbers he said you need to find the average of these two numbers. This means that you are supposed to add up the numbers and divide by the amount of numbers you added. So from this piece of information, I think mean and mid range are kind of similar... Is mid range and mean the same thing or at least similar?
• The midrange is the mean of the smallest and largest numbers. The mean is of all the numbers.
Let's you took 5 tests and got a 60, 100, 100, 100, and 100.
Your midrange would be 80. Your mean on all the tests would be 92.
• Can a range or mid-range be negative?
• The range cannot be negative. It's defined as Range = Max - Min, and Max is by definition at least as large as the Min, so Max - Min is greater than or equal to 0. Or for another take on it, the Range is a (crude) measure of variability, which must be non-negative.

The midrange can be negative. It's defined as Midrange = (Max + Min)/2. This is a measure of location (or central tendency). So if the values tend to be more on the negative side, then the midrange may be negative.
• At why does he say 4+5 equals 159
(1 vote)
• He was adding them up number by number because he said first 9+4 then 4+5 . He was just adding them seperatly.
• what is the difference between range and mid-range ?
(1 vote)
• The range is the difference between the max and min values.
The mid-range is the average of the max and min values.

## 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.