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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.