In statistics, range is the difference between the highest value in a data set and the lowest value in a data set. Range shows how spread out the values are in a series. If the range is a large number, then the values in the series are highly dispersed; 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 reach, just follow these steps.
Step 1. List the elements of your data set
To find the range of a data set, you must list all the elements in the data set so that you can identify the largest and smallest numbers. Write down all the elements. The numbers in this data set are: 14, 19, 20, 24, 25, and 28.
- It is easier to identify the largest and smallest numbers in a data set if you order the numbers from smallest to largest. In this example, the data set would be structured like this: 14, 19, 20, 24, 24, 25, 28.
- Sorting the elements in a data set will also help you perform other calculations, such as finding the mode, mean, or median of the data set.
Step 2. Identify the largest and smallest numbers in the data set
In this problem, the smallest number in the data set is 14 and the largest number is 28.
Step 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 data set, all you have to do is subtract them from each other. Subtract 14 from 25 (25 – 14) to get 11, the range of the data set.
Step 4. Label the range clearly
Once you find the range, label it clearly. This will help you avoid confusion with other statistical calculations you may have to perform, such as finding the median, mode, or mean.
- You can also interpret range in algebraic terms, but you must first understand the concept of an algebraic function, or a set of operations on known numbers. Because function operations can be performed on any number, even an unknown number, the number is denoted by a letter variable, usually x. A domain is a set of possible input values, which you can substitute for the unknown number. Thus, the range is the set of possible calculation results, which you get after entering one of the domain values and completing all the operations defined by the function. Unfortunately, there is no way to calculate the range of a function. Sometimes, graphing a function or calculating multiple values can show a clear pattern. You can also use your knowledge of the function's domain to discard possible output (calculation results) values, or narrow down the data set that represents the range.
- The median value of any statistical data set represents the median value of the data set in terms of data distribution, not range. So while you may want to assume that the median of a given data set is the range divided by 2 – or half the range of the range – this is usually not true. To find the correct median, you must sort the data elements, then look for the element in the middle of the list. This element is the median. For example, if you have a list of 29 elements, the 15th element has the same range from the beginning of the list and the end of the list, so the 15th element is the median, regardless of how the value of that element relates to the range.