In statistics, the range stands for the distance between the smallest and the largest value of a data set. The range gives an indication of how far the values spread in a series. If the range is a large number, then the values are widely spread; if it is small, then the values are close together. If you want to know how to calculate the range, follow these steps.
Step 1. List the values of your data series
To find the range of a data series, you need to list all of the individual elements so that you can determine the highest and lowest values. Write down all of the elements. The elements of our data series are: 24, 19, 20, 14, 24, 25 and 18.
- To determine the highest and lowest value, it can be helpful to enter the values in ascending order: 14, 18, 19, 20, 24, 24, 25.
- Writing down the values in order can also help with other calculations. E.g. when calculating the modal, mean or median value.
Step 2. Identify the highest and lowest values in the series
In this case, the lowest number is 14 and the highest is 25.
Step 3. Subtract the lowest number from the highest number
After you've identified them, all you have to do is subtract them from each other. So subtract 14 from 25: 25 - 24 = 11 = the range of the range.
Step 4. Clearly mark the wingspan
When you have found the span, mark it clearly as well. This way you avoid confusing them with other stochastic calculations that you may have to do for this data series.
- The median value of a statistical data set represents the “middle” of the series and not its range. Even if it sounds obvious to assume that the median of a data series divided by 2 results in the range, i.e. the middle equals the difference between the extremes, this is not always the case. Also, the range x 2 is usually not the median. To find the correct median value, you have to list all values in ascending order and then take exactly the value in the middle. This value is the median. So if you have 29 elements and have all written down in one order, the 15th value from both sides is your median, no matter how large this value is compared to the range (you can have the value 1 28 times and the value 1 once Billion, your median is still 1, but your range is …)
- You can also represent the range in algebraic terms, but first you should understand the concept of an algebraic function. Since a function can be performed on any number, including an unknown one, that number is represented by a variable, usually an “x”. The functional area (or just area) indicates which numbers can be used for this variable. The range of a function is then every possible result that can arise through the use of every possible number in the function (thus quasi the "from … to …" of the result of a function). Unfortunately, there is no “only way” to calculate this range for a function. Sometimes plotting a function or computing some values doesn't give a clear pattern. You can also use your knowledge of the area of the function to exclude possible results and narrow the data set for the range.