Calculate Range

In statistics, range represents the difference between the highest value of a data set and the lowest value of a data set. The range shows how spread out the values in a series are. If the range is a high number, then the values in the series are spread far apart; if the range is a small number, then the values in the series are close to each other. If you want to know how to calculate range, just follow these steps.

Steps

  1. List the elements of your data set. To find the range of a set, you'll need to list all of the elements of the set so that you can identify the highest and lowest numbers. Write down all of the elements. The numbers in this set are: 14, 19, 20, 24, 25, and 28.
    • It can be easier to identify the highest and lowest number in the set if you list the numbers in ascending order. In this example, the set would be rearranged like this: 14, 19, 20, 24, 24, 25, 28.
    • Listing the elements of the set in order can also help you make other calculations, such as finding the mode, mean, or median of the set.
  2. Identify the highest and lowest numbers in the set. In this case, the lowest number in the set is 14 and the highest number is 28.
  3. Subtract the smallest number in your data set from the largest number. Now that you've identified the smallest and largest numbers in the set, all you have to do is subtract them from each other. Subtract 14 from 28 (28 - 14) to get 14, the range of the set.
  4. Label the range clearly. Once you've found the range, label it clearly. This will help you avoid confusing it with any other statistical calculations that you may need to make for the set, such as finding the median, mode, or mean.



Tips

  • The median value of any statistical data set represents the "middle" of the data set in terms of the data distribution, not its range. So although you might be tempted to assume that the median of a given data set is the range divided by 2--or halfway between the extremes of the range--that usually isn't the case. To find the correct median, you must list the data elements in order, then locate the element in the middle of the list. That element is the median. For example, if you have a list of 29 elements, the 15th element will be equidistant from both the top and bottom of the ordered list, so the 15th element is the median, no matter how its value relates to the range.
  • You can also interpret "range" in algebraic terms, but first you have to grasp the concept of an algebraic function, or a set of operations on any given number. Since the function's operations can be performed on any number, even an unknown number, that number is represented by a letter variable, usually "x." The domain is the set of all possible input values you can substitute for that unknown number. The range of a function, then, is the set of all possible results you can get after inputting one of the domain values, and performing all the operations defined by the function. Unfortunately, there's no single way to calculate a function's range. Sometimes graphing the function or calculating several values will demonstrate a clear pattern. You can also use your knowledge of the function's domain to eliminate possible output values, or narrow down the data set that indicates the range.

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